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2
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3
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6
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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(MINIMUM RELEVANT VARIABLES IN LINEAR SYSTEM, MINIMUM UNSATISFYING LINEAR SUBSYSTEM, MAXIMUM HYPERPLANE CONSISTENCY)

18
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(MINIMUM 3-DEDICATED PROCESSOR SCHEDULING)

19
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20
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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31
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32
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(SHORTEST COMMON SUPERSTRING)

33
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(MINIMUM K-SPANNING TREE, MINIMUM GEOMETRIC 3-DEGREE SPANNING TREE, MINIMUM GEOMETRIC STEINER TREE, MINIMUM GEOMETRIC TRAVELING SALESPERSON)

34
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35
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J. Comput. System Sci. 54, 317-331.
(MAXIMUM SATISFYING LINEAR SUBSYSTEM, MINIMUM UNSATISFYING LINEAR SUBSYSTEM, MAXIMUM HYPERPLANE CONSISTENCY, NEAREST LATTICE VECTOR, NEAREST CODEWORD)

36
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Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 21-30.
(MINIMUM FEEDBACK ARC SET, MINIMUM LINEAR ARRANGEMENT, MINIMUM CUT LINEAR ARRANGEMENT, MAXIMUM BETWEENNESS)

37
Arora, S., Grigni, M., Karger, D., Klein, P., and Woloszyn, A. (1998),
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38
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(MINIMUM TRAVELING REPAIRMAN)

39
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Proc. 27th Ann. ACM Symp. on Theory of Comp., ACM, 284-293.
(MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM EDGE SUBGRAPH, MAXIMUM CUT, MAXIMUM DIRECTED CUT, MINIMUM K-CUT, MINIMUM MULTIWAY CUT, MINIMUM B-BALANCED CUT, MAXIMUM SET SPLITTING, MAXIMUM K-SATISFIABILITY)

40
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41
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42
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43
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44
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45
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46
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47
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48
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49
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``Buy-at-bulk network design'',
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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61
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62
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63
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64
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65
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66
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67
Bellare, M. (1993),
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68
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69
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70
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``Flow and stretch metrics for scheduling continuous job streams'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 270-279.
(MINIMUM SEQUENCING WITH RELEASE TIMES)

71
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``Complexity results and algorithms for $\{<,\leq,=\}$-constrained scheduling'',
Proc. Second Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 137-147.
(MINIMUM PRECEDENCE CONSTRAINED SCHEDULING)

72
Berger, B., and Shor, P. W. (1990),
``Approximation algorithms for the maximum acyclic subgraph problem'',
Proc. First Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 236-243.
(MINIMUM FEEDBACK ARC SET)

73
Berman, F., Johnson, D., Leighton, T., Shor, P. W., and Snyder, L. (1990),
``Generalized planar matching'',
J. Algorithms 11, 153-184.
(MAXIMUM H-MATCHING)

74
Berman, P., and DasGupta, B. (1997),
``Complexities of efficient solutions of rectilinear polygon cover problems'',
Algorithmica 17, 331-356.
(MINIMUM RECTANGLE COVER)

75
Berman, P., and Fujito, T. (1995),
``Approximating independent sets in degree 3 graphs'',
Proc. 4th Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 955, Springer-Verlag, 449-460.
(MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, MAXIMUM SET PACKING)

76
Berman, P., and Karpinski, M. (1998),
``On some tighter inapproximability results'',
Technical Report TR98-065, ECCC.
ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-065/index.html
(MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, MINIMUM METRIC TRAVELING SALESPERSON PROBLEM, MAXIMUM SATISFYING LINEAR SUBSYSTEM, MAXIMUM K-SATISFIABILITY, MINIMUM SORTING BY REVERSALS)

77
Berman, P., and Schnitger, G. (1992),
``On the complexity of approximating the independent set problem'',
Inform. and Comput. 96, 77-94.
(MAXIMUM INDUCED CONNECTED SUBGRAPH WITH PROPERTY P, LONGEST PATH WITH FORBIDDEN PAIRS, LONGEST COMMON SUBSEQUENCE, MAXIMUM BOUNDED 0-1 PROGRAMMING, MAXIMUM K-CONSTRAINT SATISFACTION, LONGEST COMPUTATION)

78
Bern, M., and Plassmann, P. (1989),
``The Steiner problem with edge lengths 1 and 2'',
Inform. Process. Lett. 32, 171-176.
(MINIMUM STEINER TREE)

79
Bernstein, D., Rodeh, M., and Gertner, I. (1989),
``Approximation algorithms for scheduling arithmetic expressions on pipelined machines'',
J. Algorithms 10, 120-139.
(MINIMUM PRECEDENCE CONSTRAINED SEQUENCING WITH DELAYS)

80
Bertsimas, D., Teo, C-P., and Vohra, R. (1996),
``On dependent randomized rounding algorithms'',
Proc. 5th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, Springer-Verlag, 330-344.
(MINIMUM EDGE COLORING, MAXIMUM SATISFIABILITY, MINIMUM K-SATISFIABILITY)

81
Blache, G., Karpinski, M., and Wirtgen, J. (1998),
``On approximation intractability of the bandwidth problem'',
Technical Report TR98-014, ECCC.
ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-014/index.html
(MINIMUM BANDWIDTH)

82
Blaha, K. D. (1992),
``Minimum bases for permutation groups: the greedy approximation'',
J. Algorithms 13, 297-306.
(MINIMUM PERMUTATION GROUP BASE)

83
Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., and Sudan, M. (1994),
``The minimum latency problem'',
Proc. 26th Ann. ACM Symp. on Theory of Comp., ACM, 163-171.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

84
Blum, A., Jiang, T., Li, M., Tromp, J., and Yannakakis, M. (1994),
``Linear approximation of shortest superstrings'',
J. ACM 41, 630-647.
(SHORTEST COMMON SUPERSTRING)

85
Blum, A., and Karger, D. (1997),
``An $\tilde{O}(n^{3/14})$-coloring algorithm for 3-colorable graphs'',
Inform. Process. Lett. 61, 49-53.
(MINIMUM GRAPH COLORING)

86
Blum, A., Ravi, R., and Vempala, S. (1996),
``A constant-factor approximation algorithm for the k-MST problem'',
Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 442-448.
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87
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``An improved lower bound on the approximability of metric TSP and approximation algorithms for the TSP with sharpened triangle inquality'',
Proc. 17th Ann. Symp. on Theoretical Aspects of Comput. Sci., Lecture Notes in Comput. Sci. 1770, Springer-Verlag, 382-394.
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88
Bodlaender, H. L., Gilbert, J. R., Hafsteinsson, H., and Kloks, T. (1995),
``Approximating treewidth, pathwidth, frontsize and shortest elimination tree'',
J. Algorithms 18, 238-255.
(MINIMUM TREE WIDTH)

89
Bonizzoni, P., Duella, M., and Mauri, G. (1994),
``Approximation complexity of longest common subsequence and shortest common supersequence over fixed alphabet'',
Technical Report 117/94, Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano.
(SHORTEST COMMON SUPERSEQUENCE, LONGEST COMMON SUBSEQUENCE)

90
Boppana, R., and Halldórsson, M. M. (1992),
``Approximating maximum independent sets by excluding subgraphs'',
Bit 32, 180-196.
(MAXIMUM CLIQUE)

91
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``Maximum renamable Horn sub-CNFs'',
Disc. Appl. Math. 96-97, 29-40.
(MAXIMUM RENAMABLE HORN SUBFORMULA)

92
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``Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem'',
Proc. 15nth Ann. Symp. on Theoretical Aspects of Comput. Sci., , Lecture Notes in Comput. Sci., Springer-Verlag, 298-308.
(MINIMUM VERTEX COVER)

93
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``Finding good approximate vertex and edge partitions is NP-hard'',
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(MINIMUM B-BALANCED CUT, MINIMUM B-VERTEX SEPARATOR)

94
Calinescu, G., Fernandes, C. G., Finkler, U., and Karloff, H. (1996),
``A better approximation algorithm for finding planar subgraphs'',
Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 16-25.
(MAXIMUM PLANAR SUBGRAPH)

95
Calinescu, G., Karloff, H., and Rabani, Y. (1998),
``An improved approximation algorithm for multiway cut'',
Proc. 30th Ann. ACM Symp. on Theory of Comp., ACM-SIAM, 48-52.
(MINIMUM MULTIWAY CUT)

96
Chakrabati, S., Phillips, C. A., Schulz, A. S., Shmoys, D. B., Stein, C., and Wein, J. (1996),
``Improved scheduling algorithms for minsum criteria'',
Proc. 23rd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1099, Springer-Verlag, 646-657.
(MINIMUM WEIGHTED COMPLETION TIME SCHEDULING)

97
Chandra, A. K., Hirschberg, D. S., and Wong, C. K. (1976),
``Approximate algorithms for some generalized knapsack problems'',
Theoretical Comput. Sci. 3, 293-304.
(MAXIMUM INTEGER M-DIMENSIONAL KNAPSACK, MAXIMUM INTEGER K-CHOICE KNAPSACK)

98
Chandra, B., and Halldórsson, M. M. (1999),
``Greedy local improvement and weighted set packing approximation'',
Proc. 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 169-176.
(MAXIMUM H-MATCHING, MAXIMUM SET PACKING)

99
Charikar, M., Chekuri, C., Cheung, T., Dai, Z., Goel, A., Guha, S., and Li, M. (1998),
``Approximation algorithms for directed Steiner problems'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 192-200.
(MINIMUM STEINER TREE, MINIMUM GENERALIZED STEINER NETWORK)

100
Chaudhary, A., and Vishwanathan, S. (1997),
``Approximation algorithms for the achromatic number'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 558-563.
(MAXIMUM ACHROMATIC NUMBER)

101
Chekuri, C., Motwani, R., Natarajan, B., and Stein, C. (1997),
``Approximation techniques for average completion time scheduling'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 609-618.
(MINIMUM SEQUENCING WITH RELEASE TIMES)

102
Chen, B. (1993),
``A better heuristic for preemptive parallel machine scheduling with batch setup times'',
SIAM J. Comp. 22, 1303-1318.
(MINIMUM PREEMPTIVE SCHEDULING WITH SET-UP TIMES)

103
Chen, B. (1994),
``Scheduling multiprocessor flow shops'', in
Advances in Optimization and Approximation, Kluwer Academic Publishers, The Netherlands, 1-8.
(MINIMUM FLOW-SHOP SCHEDULING)

104
Chen, B., Glass, C. A., Potts, C. N., and Strusevich, V. A. (1996),
``A new heuristic for three-machine flow shop scheduling'',
Oper. Res. 44, 891-898.
(MINIMUM FLOW-SHOP SCHEDULING)

105
Chen, B., Potts, C. N., and Strusevich, V. A. (1995),
``Approximation algorithms for two-machine flow shop scheduling with batch setup times'',
Math. Programming , to appear.
(MINIMUM TWO-PROCESSOR FLOW-SHOP SCHEDULING WITH BATCH SET-UP TIMES)

106
Chen, B., and Strusevich, V. A. (1993a),
``Approximation algorithms for three-machine open shop scheduling'',
ORSA J. Comput. 5, 321-326.
(MINIMUM OPEN-SHOP SCHEDULING)

107
Chen, B., and Strusevich, V. A. (1993b),
``Worst-case analysis of heuristics for open shops with parallel machines'',
European J. Oper. Res. 70, 379-390.
(MINIMUM OPEN-SHOP SCHEDULING)

108
Chen, Z.-Z. (1996),
``Practical approximation schemes for maximum induced-subgraph problems on $K_{3,3}$-free or $K_{5}$-free graphs'',
Proc. 23rd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1099, Springer-Verlag, 268-279.
(MAXIMUM INDUCED SUBGRAPH WITH PROPERTY P)

109
Cheriyan, J., and Thurimella, R. (1996),
``Approximating minimum-size k-connected spanning subgraphs via matching'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 292-301.
(MINIMUM K-VERTEX CONNECTED SUBGRAPH, MINIMUM K-EDGE CONNECTED SUBGRAPH)

110
Chlebikova, J. (1996),
``Approximability of the Maximally balanced connected partition problem in graphs'',
Inform. Process. Lett. 60, 225-230.
(MAXIMUM BALANCED CONNECTED PARTITION, MAXIMUM LEAF SPANNING TREE)

111
Choi, J., Sellen, J., and Yap, C. K. (1997),
``Approximate Euclidean shortest paths in 3-space'',
International J. Comput. Geom. Appl. 7, 271-295.
(SHORTEST PATH MOTION IN 3 DIMENSIONS)

112
Chor, B., and Sudan, M. (1998),
``A geometric approach to betweenness'',
SIAM J. Disc. Math. 11, 511-523.
(MAXIMUM BETWEENNESS)

113
Christie, D. A. (1998),
``A 3/2-approximation algorithm for Sorting by reversals'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 244-252.
(MINIMUM SORTING BY REVERSALS)

114
Christofides, N. (1976),
``Worst-case analysis of a new heuristic for the travelling salesman problem'',
Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

115
Chudak, F. A., and Shmoys, D. B. (1997),
``Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speed'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 581-590.
(MINIMUM PRECEDENCE CONSTRAINED SCHEDULING)

116
Chvátal, V. (1979),
``A greedy heuristic for the set covering problem'',
Math. Oper. Res. 4, 233-235.
(MINIMUM SET COVER)

117
Clementi, A., and Ianni, M. Di (1996),
``On the hardness of approximating optimum schedule problems in store and forward networks'',
IEEE/ACM Transaction on Networking 4, 272-280.
(MINIMUM SCHEDULE LENGTH)

118
Clementi, A., and Trevisan, L. (1996),
``Improved non-approximability results for vertex cover problems with density constraints'',
Proc. 2nd Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci. 1090, Springer-Verlag, 333-342.
(MINIMUM VERTEX COVER)

119
Cody, R. A., and Coffman, E. G., Jr (1976),
``Record allocation for minimizing expected retrieval costs on drum-like storage devices'',
J. ACM 23, 103-115.
(MINIMUM SUM OF SQUARES)

120
Coffman, E. G., Jr, Garey, M. R., and Johnson, D. S. (1997),
``Approximation algorithms for bin-packing - a survey'', in
Approximation Algorithms for NP-hard Problems, PWS Publishing Company, Boston, 46-93.
(MINIMUM BIN PACKING)

121
Coffman, E. G., Jr, Garey, M. R., Johnson, D. S., and Lapaugh, A. S. (1985),
``Scheduling file transfers'',
SIAM J. Comp. 14, 744-780.
(MINIMUM FILE TRANSFER SCHEDULING)

122
Cornuejols, G., Fisher, M., and Nemhauser, G. (1977),
``Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms'',
Management Sci. 23, 789-810.
(MAXIMUM K-FACILITY LOCATION)

123
Cowen, L. J., Goddard, W., and Jesurum, C. E. (1997),
``Coloring with defect'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 548-557.
(MINIMUM GRAPH COLORING)

124
Crama, Y., and Spieksma, F. C. R. (1992),
``Approximation algorithms for three-dimensional assignment problems with triangle inequalities'',
European J. Oper. Res. 60, 273-279.
(MINIMUM 3-DIMENSIONAL ASSIGNMENT)

125
Crescenzi, P., Kann, V., Silvestri, R., and Trevisan, L. (1999),
``Structure in approximation classes'',
SIAM J. Comp. 28, 1759-1782.
(MINIMUM EDGE COLORING, MINIMUM DEGREE SPANNING TREE, MINIMUM BIN PACKING)

126
Crescenzi, P., and Panconesi, A. (1991),
``Completeness in approximation classes'',
Inform. and Comput. 93, 241-262.
(MAXIMUM WEIGHTED SATISFIABILITY WITH BOUND)

127
Crescenzi, P., Silvestri, R., and Trevisan, L. (1994),
``On the query complexity of complete problems in approximation classes'',
Unpublished manuscript.

128
Crescenzi, P., Silvestri, R., and Trevisan, L. (1996),
``To weight or not to weight: Where is the question?'',
Proc. 4th Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 68-77.
(MAXIMUM CUT, MAXIMUM DIRECTED CUT, MAXIMUM SATISFIABILITY, MAXIMUM K-SATISFIABILITY)

129
Crescenzi, P., and Trevisan, L. (1994),
``On approximation scheme preserving reducibility and its applications'',
Proc. 14th Ann. Conf. on Foundations of Software Tech. and Theoret. Comput. Sci., Lecture Notes in Comput. Sci. 880, Springer-Verlag, 330-341.

130
Czumaj, A., and Lingas, A. (1999),
``On approximability of the minimum-cost k-connected spanning subgraph problem'',
Proc. 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 281-290.
(MINIMUM K-EDGE CONNECTED SUBGRAPH)

131
Dahlhaus, E., Johnson, D. S., Papadimitriou, C. H., Seymour, P. D., and Yannakakis, M. (1994),
``The complexity of multiterminal cuts'',
SIAM J. Comp. 23, 864-894.
(MINIMUM MULTIWAY CUT)

132
Damian-Iordache, M., and Pemmaraju, S. V. (1999),
``Hardness of approximating independent domination in circle graphs'',
Proc. 10th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 1741, Springer-Verlag, 56-69.
(MINIMUM INDEPENDENT DOMINATING SET)

133
d'Anzeo, C. (1996),
``Optimization complexity of the SCS problem given a longest common subsequence'',
Unpublished manuscript.
(SHORTEST COMMON SUPERSEQUENCE)

134
DasGupta, B., He, X., Jiang, T., Li, M., Tromp, J., and Zhang, L. (1997),
``On distances between phylogenetic trees'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 427-436.
(MINIMUM PHYLOGENETIC TREE DISTANCE)

135
Datta, A. K., and Sen, R. K. (1995),
``1-approximation algorithm for bottleneck disjoint path matching'',
Inform. Process. Lett. 55, 41-44.
(MINIMUM BOTTLENECK PATH MATCHING)

136
Di Ianni, M. (1998),
``Efficient delay routing'',
Theoretical Comput. Sci. 196, 131-151.
(MINIMUM SCHEDULE LENGTH)

137
Doddi, S., Marathe, M. V., Mirzaian, A., Moret, B. M. E., and Zhu, B. (1997),
``Map labeling and its generalizations'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 148-157.
(MAXIMUM MAP LABELING)

138
Drangmeister, K. U., Krumke, S. O., Marathe, M. V., Noltemeier, H., and Ravi, S. S. (1998),
``Modifying edges of a network to obtain short subgraphs'',
Theoretical Comput. Sci. 203, 91-121.
(MINIMUM STEINER TREE)

139
Dudek, G., Romanik, K., and Whitesides, S. (1994),
``Localizing a robot with minimum travel'',
Technical Report SOCS-94.5, McGill University.
(MINIMUM TRAVEL ROBOT LOCALIZATION)

140
Duh, R., and Fürer, M. (1997),
``Approximation of k-set cover by semi-local optimization'',
Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 256-265.
(MINIMUM GRAPH COLORING, MINIMUM CLIQUE PARTITION, MINIMUM CLIQUE COVER, MINIMUM SET COVER)

141
Eades, P., and Wormald, N. C. (1994),
``Edge crossings in drawings of bipartite graphs'',
Algorithmica 11, 379-403.
(MINIMUM CROSSING NUMBER)

142
Elkin, M., and Peleg, D. (1999),
``The hardness of approximating spanner problems'',
Technical report, Weizmann Institute.
(MINIMUM EDGE K-SPANNER)

143
Engebretsen, L. (1999),
``An explicit lower bound for TSP with distances one and two'',
Proc. 16th Ann. Symp. on Theoretical Aspects of Comput. Sci., Lecture Notes in Comput. Sci. 1563, Springer-Verlag, 373-382.
http://www.nada.kth.se/~enge/forskning-en.html
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

144
Eppstein, D. (1992),
``Approximating the minimum weight triangulation'',
Proc. Third Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 48-57.
(MINIMUM LENGTH TRIANGULATION)

145
Errico, B., and Rosati, R. (1995),
``Minimal models in propositional logics: approximation results'',
Proc. of 5th Italian Conference on Theoretical Computer Science, Word Scientific, 547-562.
(MINIMUM DISTINGUISHED ONES)

146
Even, G., Naor, J., Rao, S., and Schieber, B. (1995),
``Divide-and-conquer approximation algorithms via spreading metrics'',
Proc. 36th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 62-71.
(MINIMUM CUT LINEAR ARRANGEMENT)

147
Even, G., Naor, J., Rao, S., and Schieber, B. (1997),
``Fast approximate graph partitioning algorithms'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 639-648.
(MINIMUM B-BALANCED CUT)

148
Even, G., Naor, J., Schieber, B., and Sudan, M. (1995),
``Approximating minimum feedback sets and multi-cuts in directed graphs'',
Proc. 4th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 920, Springer-Verlag, 14-28.
(MINIMUM FEEDBACK VERTEX SET, MINIMUM FEEDBACK ARC SET)

149
Even, G., Naor, J., and Zosin, L. (1996),
``An 8-approximation algorithm for the subset feedback vertex set problem'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 310-319.
(MINIMUM FEEDBACK VERTEX SET)

150
Farach, M., Kannan, S., and Warnow, T. (1993),
``A robust model for finding optimal evolutionary trees'',
Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 137-145.
(MINIMUM SIZE ULTRAMETRIC TREE)

151
Farach, M., and Liberatore, V. (1998),
``On local register allocation'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 564-573.
(MINIMUM LOCAL REGISTER ALLOCATION)

152
Feder, T., and Greene, D. H. (1988),
``Optimal algorithms for approximate clustering'',
Proc. 20th Ann. ACM Symp. on Theory of Comp., ACM, 434-444.
(MINIMUM METRIC BOTTLENECK WANDERING SALESPERSON PROBLEM, MINIMUM K-CENTER, MINIMUM K-CLUSTERING)

153
Feige, U. (1998),
``A threshold of $\ln n$ for approximating set cover'',
J. ACM 45, 634-652.
(MINIMUM DOMINATING SET, MINIMUM SET COVER, MAXIMUM K-SATISFIABILITY)

154
Feige, U., and Goemans, M. X. (1995),
``Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT'',
Proc. 3rd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 182-189.
(MAXIMUM DIRECTED CUT, MAXIMUM K-SATISFIABILITY)

155
Feige, U., Halldórsson, M. M., and Kortsarz, G. (2000),
``Approximating the domatic number'',
Proc. 32nd Ann. ACM Symp. on Theory of Comp., ACM, .
(MAXIMUM DOMATIC PARTITION)

156
Feige, U., and Kilian, J. (1998),
``Zero knowledge and the chromatic number'',
J. Comput. System Sci. 57, 187-199.
(MINIMUM GRAPH COLORING, MINIMUM COLOR SUM)

157
Feige, U., Kortsarz, G., and Peleg, D. (1995),
``The dense k-subgraph problem'',
Unpublished manuscript.
(MAXIMUM EDGE SUBGRAPH)

158
Fekete, S., Khuller, S., Klemmstein, M., Raghavachari, B., and Young, N. (1996),
``A network-flow technique for finding low-weight bounded-degree spanning trees'',
Proc. 5th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, Springer-Verlag, 105-117.
(MINIMUM GEOMETRIC 3-DEGREE SPANNING TREE)

159
Feo, T., Goldschmidt, O., and Khellaf, M. (1992),
``One half approximation algorithms for the k-partition problem'',
Oper. Res. 40, S170-S173.
(MINIMUM K-CLUSTERING SUM)

160
Feo, T., and Khellaf, M. (1990),
``A class of bounded approximation algorithms for graph partitioning'',
Networks 20, 181-195.
(MINIMUM K-CLUSTERING SUM)

161
Fernandes, C. G. (1997),
``A better approximation ratio for the minimum k-edge-connected spanning subgraph problem'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 629-638.
(MINIMUM K-EDGE CONNECTED SUBGRAPH)

162
Fernandez de la Vega, W., and Karpinski, M. (1998),
``Polynomial time approximation of dense weighted instances of MAX-CUT'',
Technical Report TR98-064, ECCC, to appear in Randomized Structures & Algorithms.
ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-064/index.html
(MAXIMUM CUT)

163
Fernandez de la Vega, W., and Karpinski, M. (1999),
``On the approximation hardness of dense TSP and other path problems'',
Inform. Process. Lett. 70, 53-55.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM, LONGEST PATH)

164
Fernandez de la Vega, W., and Kenyon, C. (1998),
``A randomized approximation scheme for metric MAX-CUT'',
Proc. 39th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 468-471.
(MAXIMUM CUT)

165
Fernandez de la Vega, W., and Zissimopoulos, V. (1991),
``An approximation scheme for strip-packing of rectangles with bounded dimensions'',
Technical Report 713, Laboratoire de Recherche en Informatique, Université de Paris, Orsay.
(MINIMUM HEIGHT TWO DIMENSIONAL PACKING)

166
Fialko, S., and Mutzel, P. (1998),
``A new approximation algorithm for the Planar augmentation problem'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 260-269.
(MINIMUM BICONNECTIVITY AUGMENTATION)

167
Floréen, P., and Orponen, P. (1993),
``Attraction radii in binary Hopfield nets are hard to compute'',
Neural Comput. 5, 812-821.
(MINIMUM ATTRACTION RADIUS FOR BINARY HOPFIELD NET)

168
Formann, M., and Wagner, F. (1991),
``A packing problem with applications to lettering of maps'',
Proc. 7th Ann. ACM Symp. Comput. Geom., ACM, 281-288.
(MAXIMUM MAP LABELING)

169
Fraser, C. B., and Irving, R. W. (1995),
``Approximation algorithms for the shortest common supersequence'',
Nordic J. Comp. 2, 303-325.
(SHORTEST COMMON SUPERSEQUENCE)

170
Fraser, C. B., Irving, R. W., and Middendorf, M. (1996),
``Maximal common subsequences and minimal common supersequences'',
Inform. and Comput. 124, 145-153.
(LONGEST COMMON SUBSEQUENCE)

171
Frederickson, G. N., Hecht, M. S., and Kim, C. E. (1978),
``Approximation algorithms for some routing problems'',
SIAM J. Comp. 7, 178-193.
(MINIMUM METRIC TRAVELING K-SALESPERSON PROBLEM, MINIMUM K-CHINESE POSTMAN PROBLEM, MINIMUM STACKER CRANE PROBLEM, MINIMUM K-STACKER CRANE PROBLEM)

172
Frederickson, G. N., and Jájá, J. (1981),
``Approximation algorithms for several graph augmentation problems'',
SIAM J. Comp. 10, 270-283.
(MINIMUM BICONNECTIVITY AUGMENTATION, MINIMUM STRONG CONNECTIVITY AUGMENTATION)

173
Frederickson, G. N., and Jájá, J. (1982),
``On the relationship between the biconnectivity augmentation and traveling salesman problems'',
Theoretical Comput. Sci. 19, 189-201.
(MINIMUM K-VERTEX CONNECTED SUBGRAPH, MINIMUM BICONNECTIVITY AUGMENTATION)

174
Frederickson, G. N., and Solis-Oba, R. (1996),
``Increasing the weight of minimum spanning trees'',
Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 539-546.
(MAXIMUM MINIMUM SPANNING TREE DELETING K EDGES)

175
Frieze, A., Galbiati, G., and Maffioli, F. (1982),
``On the worst-case performance of some algorithms for the asymmetric traveling salesman problem'',
Networks 12, 23-39.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

176
Frieze, A., and Jerrum, M. (1997),
``Improved approximation algorithms for MAX k-CUT and MAX BISECTION'',
Algorithmica 18, 67-81.
(MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM K-CUT)

177
Fujito, T. (1996),
``A unified local ratio approximation of node-deletion problems'',
Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 167-178.
(MINIMUM VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY P)

178
Fürer, M., and Raghavachari, B. (1994),
``Approximating the minimum-degree Steiner tree to within one of optimal'',
J. Algorithms 17, 409-423.
(MINIMUM DEGREE SPANNING TREE)

179
Galbiati, G., Maffioli, F., and Morzenti, A. (1994),
``A short note on the approximability of the maximum leaves spanning tree problem'',
Inform. Process. Lett. 52, 45-49.
(MAXIMUM LEAF SPANNING TREE)

180
Galbiati, G., Maffioli, F., and Morzenti, A. (1995),
``On the approximability of some maximum spanning tree problems'',
Proc. 2nd Int. Symp. Latin American Theoretical Informatics, Lecture Notes in Comput. Sci. 911, Springer-Verlag, 300-311.
(MAXIMUM LEAF SPANNING TREE)

181
Garey, M. R., and Graham, R. L. (1975),
``Bounds for multiprocessor scheduling with resource constraints'',
SIAM J. Comp. 4, 187-200.
(MINIMUM RESOURCE CONSTRAINED SCHEDULING)

182
Garey, M. R., and Johnson, D. S. (1979),
Computers and Intractability: A guide to the theory of NP-completeness,
W. H. Freeman and Company, San Francisco.
(MINIMUM DEGREE SPANNING TREE, MINIMUM BIN PACKING)

183
Garg, A., and Tamassia, R. (1994),
``On the computational complexity of upward and rectilinear planarity testing'',
Proc. DIMACS Int. Workshop on Graph Drawing, Lecture Notes in Comput. Sci. 894, Springer-Verlag, 286-297.
(MINIMUM BEND NUMBER)

184
Garg, N. (1996),
``A 3-approximation for the minimum tree spanning k vertices'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 302-309.
(MINIMUM K-SPANNING TREE, MINIMUM TRAVELING REPAIRMAN)

185
Garg, N., Konjevod, G., and Ravi, R. (1998),
``A polylogarithmic approximation algorithm for the group Steiner tree problem'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 253-259.
(MINIMUM STEINER TREE)

186
Garg, N., Santosh, V. S., and Singla, A. (1993),
``Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques'',
Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 103-111.
(MINIMUM K-VERTEX CONNECTED SUBGRAPH)

187
Garg, N., Saran, H., and Vazirani, V. (1994),
``Finding separator cuts in planar graphs within twice the optimal'',
Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 14-23.
(MINIMUM B-BALANCED CUT)

188
Garg, N., Vazirani, V. V., and Yannakakis, M. (1994),
``Multiway cuts in directed and node weighted graphs'',
Proc. 21st Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 820, Springer-Verlag, 487-498.
(MINIMUM VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY P, MINIMUM VERTEX K-CUT, MINIMUM MULTIWAY CUT, MINIMUM MULTI-CUT)

189
Garg, N., Vazirani, V. V., and Yannakakis, M. (1996),
``Approximate max-flow min-(multi)cut theorems and their applications'',
SIAM J. Comp. 25, 235-251.
(MINIMUM EDGE DELETION K-PARTITION, MINIMUM MULTI-CUT, MINIMUM EQUIVALENCE DELETION)

190
Garg, N., Vazirani, V. V., and Yannakakis, M. (1997),
``Primal-dual approximation algorithms for integral flow and multicut in trees'',
Algorithmica 18, 3-20.
(MINIMUM MULTI-CUT, MAXIMUM INTEGRAL K-MULTICOMMODITY FLOW ON TREES, MINIMUM SET COVER)

191
Gens, G. V., and Levner, E. V. (1979),
``Computational complexity of approximation algorithms for combinatorial problems'',
Proc. 8th International Symp. on Mathematical Foundations of Comput. Sci., Lecture Notes in Comput. Sci. 74, Springer-Verlag, 292-300.
(MAXIMUM KNAPSACK, MAXIMUM INTEGER K-CHOICE KNAPSACK)

192
Gergov, J. (1996),
``Approximation algorithms for dynamic storage allocation'',
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193
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194
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``Improved approximation algorithms for network design problems'',
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195
Goemans, M. X., and Kleinberg, J. M. (1996),
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196
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197
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SIAM J. Comp. 24, 296-317.
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198
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199
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``Primal-dual approximation algorithms for feedback problems in planar graphs'',
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200
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201
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``Polynomial algorithm for the k-cut problem'',
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202
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203
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204
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205
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206
Grigoriadis, M. D., and Khachiyan, L. G. (1994),
``Fast approximation schemes for convex programs with many blocks and coupling constraints'',
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207
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``Close approximation of minimum rectangular coverings'',
J. Combinatorial Optimization 3, 437-452.
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208
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``Approximation algorithms for connected dominating sets'',
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209
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210
Gusfield, D., and Pitt, L. (1992),
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211
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212
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213
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``Approximation algorithms for minimum sum p-clustering'',
Disc. Appl. Math. 89, 125-142.
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214
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``Approximation algorithms for minimum k-cut'',
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215
Guttmann-Beck, N., Hassin, R., Khuller, S., and Raghavachari, B. (1999),
``Approximation algorithms with bounded performance guarantees for the clustered traveling salesman problem'',
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216
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``On-line and off-line approximation algorithms'',
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217
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218
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``Low-degree graph partitioning via local search with applications to constraint satisfaction, max cut, and 3-coloring'',
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219
Halldórsson, M. M. (1993a),
``A still better performance guarantee for approximate graph coloring'',
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220
Halldórsson, M. M. (1993b),
``Approximating the minimum maximal independence number'',
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221
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``personal communication'',
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222
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223
Halldórsson, M. M. (1995b),
``Approximation via partitioning'',
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224
Halldórsson, M. M. (1999a),
``Approximations of weighted independent set and hereditary subset problems'',
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225
Halldórsson, M. M., Iwano, K., Katoh, N., and Tokuyama, T. (1995),
``Finding subsets maximizing minimum structures'',
Proc. 6th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 150-159.
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226
Halldórsson, M. M., and Kortsarz, G. (1999),
``Multicoloring planar graphs and partial k-trees'',
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227
Halldórsson, M. M., Kortsarz, G., and Nutov, Z. (1999),
``Transforming a preemptive coloring into a non-preemptive one with applications'',
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228
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``Multi-coloring trees'',
Proc. 5th Ann. Int. Conf. on Computing and Combinatorics, , Lecture Notes in Comput. Sci., Springer-Verlag, 271-280.
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229
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``Independent sets with domination constraints'',
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230
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``Approximation and special cases of common subtrees and editing distance'',
Proc. 7th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 1178, Springer-Verlag, 75-84.
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231
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232
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Proc. 11th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, .
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233
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``Lower bounds on learning decision lists and trees'',
Inform. and Comput. 126, 114-122.
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234
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``Bandwidth minimization: an approximation algorithm for caterpillars'',
Math. Systems Theory 24, 169-177.
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235
Hassin, R. (1992),
``Approximation schemes for the restricted shortest path problem'',
Math. Oper. Res. 17, 36-42.
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236
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``Approximation algorithms for hitting objects with straight lines'',
Disc. Appl. Math. 30, 29-42.
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237
Hassin, R., and Rubinstein, S. (1994),
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238
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239
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240
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241
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242
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243
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244
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``A well-characterized approximation problem'',
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245
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246
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SIAM J. Comp. 11, 555-556.
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247
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Math. Programming 22, 148-162.
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248
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249
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250
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251
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``Approximation schemes for covering and packing problems in image processing and VLSI'',
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252
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``Fast approximation algorithms for a nonconvex covering problem'',
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253
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254
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``A unified approach to approximation algorithms for bottleneck problems'',
J. ACM 33, 533-550.
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255
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``Using dual approximation algorithms for scheduling problems: theoretical and practical results'',
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256
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``A polynomial approximation scheme for machine scheduling on uniform processors: using the dual approach'',
SIAM J. Comp. 17, 539-551.
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257
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``Approximating maximum independent sets in uniform hypergraphs'',
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258
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SIAM J. Comp. 10, 718-720.
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259
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260
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261
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``Exact and approximate algorithms for scheduling nonidentical processors'',
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262
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``Easy and hard bottleneck location problems'',
Disc. Appl. Math. 1, 209-216.
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263
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``Approximation schemes using L-reductions'',
Proc. 14th Ann. Conf. on Foundations of Software Tech. and Theoret. Comput. Sci., Lecture Notes in Comput. Sci. 880, Springer-Verlag, 342-353.
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264
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``Nc-approximation schemes for NP- and PSPACE-hard problems for geometric graphs'',
J. Algorithms 26, 238-274.
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265
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``On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems'',
SIAM J. Disc. Math. 2, 68-72.
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266
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``Fast approximation for the knapsack and sum of subset problems'',
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267
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``The complexity of approximating the class Steiner tree problem'',
Proc. 18th Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 570, Springer-Verlag, 85-96.
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268
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``Constraint satisfaction and maximum clique'',
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269
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270
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271
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274
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275
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Proc. 21st Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 820, Springer-Verlag, 191-202.
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276
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277
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279
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280
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``Maximum bounded 3-dimensional matching is MAX SNP-complete'',
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281
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Proc. 9th Ann. Symp. on Theoretical Aspects of Comput. Sci., Lecture Notes in Comput. Sci. 577, Springer-Verlag, 377-388.
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282
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283
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``Maximum bounded H-matching is MAX SNP-complete'',
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284
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285
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``Strong lower bounds on the approximability of some NPO PB-complete maximization problems'',
Proc. 20th International Symp. on Mathematical Foundations of Comput. Sci., Lecture Notes in Comput. Sci. 969, Springer-Verlag, 227-236.
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286
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287
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``Approximability of maximum splitting of k-sets and some other APX-complete problems'',
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288
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289
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290
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292
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293
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294
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295
Karpinski, M., and Wirtgen, J. (1997),
``On approximation hardness of the bandwidth problem'',
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296
Karpinski, M., Wirtgen, J., and Zelikovsky, A. (1997),
``An approximation algorithm for the bandwidth problem on dense graphs'',
Technical Report TR97-017, ECCC.
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297
Karpinski, M., and Zelikovsky, A. (1997),
``Approximating dense cases of covering problems'',
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298
Karuno, Y., Nagamochi, H., and Ibaraki, T. (1993),
``Vehicle scheduling on a tree with release and handling times'',
Proc. 4th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 762, Springer-Verlag, 486-495.
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299
Kavvadias, D., Papadimitriou, C. H., and Sideri, M. (1993),
``On Horn envelopes and hypergraph transversals'',
Proc. 4th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 762, Springer-Verlag, 399-405.
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300
Kellerer, H., Tautenhahn, T., and Woeginger, G. J. (1996),
``Approximability and nonapproximability results for minimizing total flow time on a single machine'',
Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 418-426.
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301
Kenyon, C., and Rémila, E. (1996),
``Approximate strip packing'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 31-36.
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302
Khanna, S. (1997),
``A polynomial time approximation scheme for the SONET ring loading problem'',
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303
Khanna, S., Linial, N., and Safra, S. (1993),
``On the hardness of approximating the chromatic number'',
Proc. 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 250-260.
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304
Khanna, S., and Motwani, R. (1996),
``Toward a syntactic characterization of PTAS'',
Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 329-337.
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305
Khanna, S., Motwani, R., Sudan, M., and Vazirani, U. (1999),
``On syntactic versus computational views of approximability'',
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306
Khanna, S., Muthukrishnan, S., and Paterson, M. (1998),
``On approximating rectangle tiling and packing'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 384-393.
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307
Khanna, S., Muthukrishnan, S., and Skiena, S. (1997),
``Efficient array partitioning'',
Proc. 24th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1256, Springer-Verlag, 616-626.
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308
Khanna, S., Sudan, M., and Trevisan, L. (1997),
``Constraint satisfaction: the approximability of minimization problems'',
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309
Khanna, S., Sudan, M., and Williamson, D. P. (1997),
``A complete classification of the approximability of maximization problems derived from Boolean constraint satisfaction'',
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310
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311
Khuller, S., Pless, R., and Sussmann, Y. J. (1997),
``Fault tolerant k-center problems'',
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312
Khuller, S., and Raghavachari, B. (1996),
``Improved approximation algorithms for uniform connectivity problems'',
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313
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``Localization in graphs'',
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314
Khuller, S., Raghavachari, B., and Young, N. (1993),
``Maintaining directed reachability with few edges'',
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315
Khuller, S., Raghavachari, B., and Young, N. (1995),
``Approximating the minimum equivalent digraph'',
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316
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``Low degree spanning trees of small weight'',
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317
Khuller, S., Raghavachari, B., and Young, N. (1996b),
``On strongly connected digraphs with bounded cycle length'',
Disc. Appl. Math. 69, 281-289.
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318
Khuller, S., and Sussmann, Y. J. (1996),
``The capacitated k-center problem'',
Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 152-166.
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319
Khuller, S., and Thurimella, R. (1993),
``Approximation algorithms for graph augmentation'',
J. Algorithms 14, 214-225.
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320
Khuller, S., and Vishkin, U. (1994),
``Biconnectivity approximations and graph carvings'',
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321
Kim, S., and McNaughton, R. (1993),
``Computing the order of a locally testable automaton'',
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322
Klein, P., Agrawal, A., Ravi, R., and Rao, S. (1990),
``Approximation through multicommodity flow'',
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323
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``Excluded minors, network decomposition, and multicommodity flow'',
Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 682-690.
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324
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``Approximations for the disjoint paths problem in high-diameter planar networks'',
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325
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``Single-source unsplittable flow'',
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326
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``Approximating the bandwidth for asteroidal triple-free graphs'',
Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 434-447.
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327
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``An optimal approximation algorithm for the rectilinear m-center problem'',
Algorithmica 5, 341-352.
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328
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``The minimum satisfiability problem'',
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329
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``Logical definability of NP optimization problems'',
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330
Kolaitis, P. G., and Thakur, M. N. (1995),
``Approximation properties of NP minimization classes'',
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331
Kolliopoulos, S. G., and Stein, C. (1997),
``Improved approximation algorithms for unsplittable flow problems'',
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332
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333
Kortsarz, G., and Peleg, D. (1994),
``Generating sparse 2-spanners'',
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334
Kortsarz, G., and Peleg, D. (1995),
``Approximation algorithms for minimum time broadcast'',
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335
Kortsarz, G., and Peleg, D. (1997),
``Approximating shallow-light trees'',
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336
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``Generating low-degree 2-spanners'',
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337
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``Long tours and short superstrings'',
Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 166-177.
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338
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339
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``Searching a fixed graph'',
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340
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``Approximate coloring of uniform hypergraphs'',
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341
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342
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``Improving spanning trees by upgrading nodes'',
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343
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``Approximating circular arc colouring and bandwidth allocation in all-optical ring networks'',
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344
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345
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346
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347
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349
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350
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352
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353
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``Quasi-greedy triangulations approximating the minimum weight triangulation'',
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354
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355
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356
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``On three-dimensional packing'',
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357
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``Towards a DNA sequencing theory'',
Proc. 31st Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 125-134.
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358
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``Finding similar regions in many strings'',
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359
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360
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361
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``A separator theorem for planar graphs'',
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362
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``The power of local optimization: Approximation algorithms for maximum-leaf spanning tree'',
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363
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``Scheduling malleable and nonmalleable parallel tasks'',
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364
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365
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366
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``On the inapproximability of disjoint paths and minimum Steiner forest with bandwidth constraints'',
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367
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``Derandomizing semidefinite programming based approximation algorithms'',
Proc. 36th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 162-169.
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368
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``Approximating the minimum net expansion: near optimal solutions to circuit partitioning problems'',
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369
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Proc. 22nd Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 1197, Springer-Verlag, 308-322.
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370
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371
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``Efficient approximation algorithms for domatic partition and on-line coloring of circular arc graphs'',
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372
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``Bicriteria network design problems'',
Proc. 22nd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 944, Springer-Verlag, 487-498.
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373
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``Graph inference from a walk for trees of bounded degree 3 is NP-complete'',
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374
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``Approximation algorithms for geometric tour and network design problems'',
Proc. 11th Ann. ACM Symp. Comput. Geom., ACM, 360-369.
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375
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376
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``On the approximation of finding various minimal, maximal, and consistent sequences'',
Proc. 5th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 834, Springer-Verlag, 306-314.
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377
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``Computing a shortest k-link path in a polygon'',
Proc. 33rd Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 573-582.
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378
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``Separation and approximation of polyhedral objects'',
Proc. Third Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 296-306.
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379
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``Scheduling jobs with communication delays: using infeasible solutions for approximation'',
Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 76-90.
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380
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``Ramsey numbers and an approximation algorithm for the vertex cover problem'',
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381
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382
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383
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``A 2-approximation algorithm for the directed multiway cut problem'',
Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 548-553.
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384
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385
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Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 639-648.
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386
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387
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388
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Technical Report C-1987-28, Department of Computer Science, University of Helsinki.
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389
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390
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391
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392
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Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 511-520.
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393
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``Optimization, approximation, and complexity classes'',
J. Comput. System Sci. 43, 425-440.
(MINIMUM VERTEX COVER, MINIMUM DOMINATING SET, MINIMUM FEEDBACK ARC SET, MAXIMUM INDEPENDENT SET, MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM CUT, MAXIMUM DIRECTED CUT, MINIMUM SET COVER, MAXIMUM SATISFIABILITY, MAXIMUM K-SATISFIABILITY, MAXIMUM NOT-ALL-EQUAL 3-SATISFIABILITY)

394
Papadimitriou, C. H., and Yannakakis, M. (1993),
``The traveling salesman problem with distances one and two'',
Math. Oper. Res. 18, 1-11.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

395
Park, J. K., and Phillips, C. A. (1993),
``Finding minimum-quotient cuts in planar graphs'',
Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 766-775.
(MINIMUM QUOTIENT CUT)

396
Paz, A., and Moran, S. (1981),
``Non deterministic polynomial optimization problems and their approximations'',
Theoretical Comput. Sci. 15, 251-277.
(MINIMUM CLIQUE PARTITION)

397
Peleg, D., and Reshef, E. (1998),
``Deterministic polylog approximation for minimum communication spanning trees'',
Proc. 25th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1443, Springer-Verlag, 670-679.
(MINIMUM COMMUNICATION COST SPANNING TREE)

398
Peleg, D., Schechtman, G., and Wool, A. (1993),
``Approximating bounded 0-1 integer linear programs'',
Proc. 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 69-77.
(MINIMUM SET COVER)

399
Petrank, E. (1992),
``The hardness of approximation: gap location'',
Technical Report 754, Computer Science Department, Technion, Israel Institute of Technology, Haifa, Israel.
(NEAREST CODEWORD)

400
Petrank, E. (1994),
``The hardness of approximation: gap location'',
Computational Complexity 4, 133-157.
(MINIMUM VERTEX COVER, MINIMUM EDGE COLORING, MAXIMUM SET SPLITTING)

401
Phillips, C., Stein, C., and Wein, J. (1995),
``Scheduling jobs that arrive over time'',
Proc. 4th Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 955, Springer-Verlag, 86-97.
(MINIMUM WEIGHTED COMPLETION TIME SCHEDULING)

402
Phillips, C. A. (1993),
``The network inhibition problem'',
Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 776-785.
(MINIMUM NETWORK INHIBITION ON PLANAR GRAPHS, SHORTEST WEIGHT-CONSTRAINED PATH)

403
Pitt, L., and Warmuth, M. K. (1993),
``The minimum consistent DFA problem cannot be approximated within any polynomial'',
J. ACM 40, 95-142.
(MINIMUM CONSISTENT FINITE AUTOMATON)

404
Plesník, J. (1980),
``On the computational complexity of centers locating in a graph'',
Aplikace Matematiky 25, 445-452.
(MINIMUM K-CENTER)

405
Plesník, J. (1981),
``The complexity of designing a network with minimum diameter'',
Networks 11, 77-85.
(MINIMUM DIAMETER SPANNING SUBGRAPH)

406
Plesník, J. (1982),
``Complexity of decomposing graphs into factors with given diameters or radii'',
Math. Slovaca 32, 379-388.
(MINIMUM DIAMETERS DECOMPOSITION)

407
Plesník, J. (1987),
``A heuristic for the p-center problem in graphs'',
Disc. Appl. Math. 17, 263-268.
(MINIMUM K-CENTER)

408
Plesník, J. (1988),
``Two heuristics for the absolute p-center problem in graphs'',
Math. Slovaca 38, 227-233.
(MINIMUM K-CENTER)

409
Provan, J. S. (1988),
``An approximation scheme for finding Steiner trees with obstacles'',
SIAM J. Comp. 17, 920-934.
(MINIMUM GEOMETRIC STEINER TREE)

410
Queyranne, M. (1985),
``Bounds for assembly line balancing heuristics'',
Oper. Res. 33, 1353-1359.
(MINIMUM BIN PACKING)

411
Queyranne, M. (1986),
``Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems'',
Oper. Res. Lett. 4, 231-234.
(MINIMUM QUADRATIC 0-1 ASSIGNMENT)

412
Rabani, Y. (1996),
``Path coloring on the mesh'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 400-409.
(MAXIMUM DISJOINT CONNECTING PATHS)

413
Raghavachari, B., and Veerasamy, J. (1999),
``A 3/2-approximation algorithm for the mixed postman problem'',
SIAM J. Disc. Math. 12, 425-433.
(MINIMUM CHINESE POSTMAN FOR MIXED GRAPHS)

414
Raghavan, P., and Thompson, C. D. (1991),
``Multiterminal global routing: A deterministic approximation scheme'',
Algorithmica 6, 73-82.
(MINIMUM RECTILINEAR GLOBAL ROUTING)

415
Raghavan, P., and Upfal, E. (1994),
``Efficient routing in all-optical networks'',
Proc. 26th Ann. ACM Symp. on Theory of Comp., ACM, 134-143.
(MAXIMUM DISJOINT CONNECTING PATHS)

416
Rao, S., and Richa, A. W. (1998),
``New approximation techniques for some ordering problems'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 211-218.
(MINIMUM INTERVAL GRAPH COMPLETION, MINIMUM LINEAR ARRANGEMENT, MINIMUM STORAGE-TIME SEQUENCING)

417
Ravi, R. (1994a),
``A primal-dual approximation algorithm for the Steiner forest problem'',
Inform. Process. Lett. 50, 185-190.
(MINIMUM STEINER TREE)

418
Ravi, R. (1994b),
``Rapid rumor ramification: approximating the minimum broadcast time'',
Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 202-213.
(MINIMUM BROADCAST TIME)

419
Ravi, R., Sundaram, R., Marathe, M. V., Rosenkrantz, D. J., and Ravi, S. S. (1994),
``Spanning trees short or small'',
Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 546-555.
(MINIMUM K-SPANNING TREE)

420
Ravi, R., and Williamson, D. (1997),
``An approximation algorithm for minimum-cost vertex-connectivity problems'',
Algorithmica 18, 21-43.
(MINIMUM K-VERTEX CONNECTED SUBGRAPH)

421
Ravi, S. S., Rosenkrantz, D. J., and Tayi, G. K. (1991),
``Facility dispersion problems: heuristics and special cases'',
Proc. 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 519, Springer-Verlag, 355-366.
(MAXIMUM K-FACILITY DISPERSION)

422
Rayward-Smith, V. J. (1987),
``Net scheduling with unit interprocessor communication delays'',
Disc. Appl. Math. 18, 55-71.
(MINIMUM PRECEDENCE CONSTRAINED SCHEDULING)

423
Raz, R., and Safra, S. (1997),
``A sub-constant error-probability low-degree test, and sub-constant error-probability PCP characterization of NP'',
Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 475-484.
(MINIMUM DOMINATING SET, MINIMUM SET COVER)

424
Robins, G., and Zelikovsky, A. (2000),
``Improved steiner tree approximation in graphs'',
Proc. 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 770-779.
(MINIMUM STEINER TREE)

425
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``On the sum coloring problem on interval graphs'',
Algorithmica 23, 109-126.
(MINIMUM COLOR SUM)

426
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``P-complete approximation problems'',
J. ACM 23, 555-565.
(MINIMUM VERTEX DISJOINT CYCLE COVER, MINIMUM EDGE DELETION K-PARTITION, MINIMUM K-CLUSTERING SUM, MINIMUM GENERALIZED 0-1 ASSIGNMENT, MINIMUM QUADRATIC 0-1 ASSIGNMENT)

427
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``Buy-at-bulk network design: approximating the single-sink edge installation problem'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 619-628.
(MINIMUM SINGLE-SINK EDGE INSTALLATION)

428
Saran, H., and Vazirani, V. (1991),
``Finding k-cuts within twice the optimal'',
Proc. 32nd Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 743-751.
(MINIMUM K-CUT)

429
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``Depth-first search and the vertex cover problem'',
Inform. Process. Lett. 14, 233-237.
(MINIMUM VERTEX COVER)

430
Schiermeyer, I. (1994),
``Reverse-fit: a 2-optimal algorithm for packing rectangles'',
Proc. 2nd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 855, Springer-Verlag, 290-299.
(MINIMUM HEIGHT TWO DIMENSIONAL PACKING)

431
Schulz, A. S., and Skutella, M. (1996),
``Scheduling-LPs bear probabilities: Randomized approximations for Min-sum criteria'',
Technical Report 533/1996, Technical University of Berlin, Department of Mathematics.
(MINIMUM SEQUENCING WITH RELEASE TIMES)

432
Schulz, A. S., and Skutella, M. (1997a),
``Scheduling-LPs bear probabilities: randomized approximation for Min-sum criteria'',
Proc. 5th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1284, Springer-Verlag, 416-429.
(MINIMUM WEIGHTED COMPLETION TIME SCHEDULING)

433
Schulz, A. S., and Skutella, M. (1997b),
``Random-based scheduling: New approximations and LP lower bounds'',
Proc. 1st Symp. on Randomization and Approximation Techniques in Comput. Sci., Lecture Notes in Comput. Sci. 1269, Springer-Verlag, 119-133.
(MINIMUM SEQUENCING WITH RELEASE TIMES, MINIMUM WEIGHTED COMPLETION TIME SCHEDULING)

434
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``An algorithm with an estimate for the traveling salesman problem of the maximum'',
Upravlyaemye Sistemy 25, 80-86.
(MINIMUM TRAVELING SALESPERSON)

435
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``Packing directed circuits fractionally'',
Combinatorica 15, 281-288.
(MINIMUM FEEDBACK VERTEX SET)

436
Seymour, P. D., and Thomas, R. (1994),
``Call routing and the rat catcher'',
Combinatorica 14, 217-241.
(MINIMUM ROUTING TREE CONGESTION)

437
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``Noah's bagels - some combinatorial aspects'',
Proc. 1st Int. Conf. on Fun with Algorithms, , .
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(MAXIMUM CLASS-CONSTRAINED KNAPSACK)

438
Shamir, R., and Tsur, D. (1998),
``The maximum subforest problem: Approximation and exact algorithms'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 394-399.
(MAXIMUM SUBFOREST)

439
Shmoys, D. B. (1997),
``Cut problems and their application to divide-and-conquer'', in
Approximation Algorithms for NP-hard Problems, PWS Publishing Company, Boston, 192-235.
(MINIMUM B-BALANCED CUT)

440
Shmoys, D. B., Stein, C., and Wein, J. (1994),
``Improved approximation algorithms for shop scheduling problems'',
SIAM J. Comp. 23, 617-632.
(MINIMUM JOB SHOP SCHEDULING)

441
Shmoys, D. B., and Tardos, É. (1993),
``Scheduling unrelated machines with costs'',
Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 448-454.
(MINIMUM MULTIPROCESSOR SCHEDULING)

442
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``New worst-case results for the bin-packing problem'',
Naval Res. Logistics 41, 579-585.
(MINIMUM BIN PACKING)

443
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``Approximation algorithms for channel assignment in cellular radio networks'',
Proc. 7th Int. Symp. on Fundamentals of Computation Theory, Lecture Notes in Comput. Sci. 380, Springer-Verlag, 405-416.
(MAXIMUM CHANNEL ASSIGNMENT)

444
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``On approximate solutions for combinatorial optimization problems'',
SIAM J. Disc. Math. 3, 294-310.
(MINIMUM CLIQUE COVER, MINIMUM COMPLETE BIPARTITE SUBGRAPH COVER, MINIMUM CONSISTENT FINITE AUTOMATON)

445
Skutella, M. (1997),
``Approximation algorithms for the discrete time-cost tradeoff problem'',
Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 501-508.
(MINIMUM TIME-COST TRADEOFF)

446
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``Improved approximations of packing and covering problems'',
Proc. 27th Ann. ACM Symp. on Theory of Comp., ACM, 268-276.
(MINIMUM SET COVER, MAXIMUM PACKING INTEGER PROGRAMMING, MINIMUM COVERING INTEGER PROGRAMMING)

447
Srinivasan, A. (1997),
``Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems'',
Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 416-425.
(MAXIMUM DISJOINT CONNECTING PATHS)

448
Srivastav, A., and Stangier, P. (1994),
``Tight approximations for resource constrained scheduling problems'',
Proc. 2nd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 855, Springer-Verlag, 307-318.
(MINIMUM RESOURCE CONSTRAINED SCHEDULING)

449
Tamir, A. (1991),
``Obnoxious facility location on graphs'',
SIAM J. Disc. Math. 4, 550-567.
(MAXIMUM K-FACILITY DISPERSION)

450
Tarhio, J., and Ukkonen, E. (1988),
``A greedy approximation algorithm for constructing shortest common superstrings'',
Theoretical Comput. Sci. 57, 131-145.
(SHORTEST COMMON SUPERSTRING)

451
Trevisan, L. (1996),
``Positive linear programming, parallel approximation and PCPs'',
Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 62-75.
(MAXIMUM K-CONSTRAINT SATISFACTION)

452
Trevisan, L. (1997),
``When Hamming meets Euclid: the approximability of geometric TSP and MST'',
Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 21-29.
(MINIMUM GEOMETRIC TRAVELING SALESPERSON)

453
Trevisan, L., Sorkin, G. B., Sudan, M., and Williamson, D. P. (1996),
``Gadgets, approximation, and linear programming'',
Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 617-626.
(MAXIMUM K-SATISFIABILITY)

454
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``Scheduling parallel tasks to minimize average response time'',
Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 112-121.
(MINIMUM RESOURCE CONSTRAINED SCHEDULING)

455
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``Approximation algorithms for the shortest common superstring problem'',
Inform. and Comput. 83, 1-20.
(SHORTEST COMMON SUPERSTRING)

456
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``On the largest common subgraph problem'',
Unpublished manuscript.
(MAXIMUM COMMON SUBGRAPH)

457
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``On the hardness of approximating some optimization problems that are supposedly easier than Max Clique'',
Combinatorics, Probability and Computing 4, 167-180.
(MAXIMUM H-MATCHING, MAXIMUM INDEPENDENT SET, MAXIMUM K-CONSTRAINT SATISFACTION)

458
Vishwanathan, S. (1992),
``An approximation algorithm for the asymmetric travelling salesman problem with distances one and two'',
Inform. Process. Lett. 44, 297-302.
(MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

459
Vishwanathan, S. (1996),
``An $o(\log^*n)$ approximation algorithm for the asymmetric p-center problem'',
Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 1-5.
(MINIMUM K-CENTER)

460
Vishwanathan, S. (1996),
``Personal communication'',
Unpublished manuscript.
(MAXIMUM INDEPENDENT SET)

461
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``On an estimate of the chromatic class of a p-graph'',
Diskret. Analiz. 3, 23-30.
(MINIMUM EDGE COLORING)

462
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``An efficient and effective approximation algorithm for the map labeling problem'',
Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 420-433.
(MAXIMUM MAP LABELING)

463
Wang, Q., and Cheng, K. H. (1990),
``A heuristic algorithm for the k-center problem with cost and usage weights'',
Technical Report TR #UH-CS-90-15, Computer Science Department, Houston University.
(MINIMUM K-SUPPLIER)

464
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``Assembly line balancing as generalized bin packing'',
Oper. Res. Lett. 1, 56-58.
(MINIMUM BIN PACKING)

465
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``A primal-dual approximation algorithm for generalized Steiner network problems'',
Combinatorica 15, 435-454.
(MINIMUM GENERALIZED STEINER NETWORK)

466
Williamson, D. P., Hall, L. A., Hoogeveen, J. A., Hurkens, C. A. J., Lenstra, J. K., and Shmoys, D. B. (1994),
``Short shop schedules'',
Unpublished manuscript.
(MINIMUM OPEN-SHOP SCHEDULING, MINIMUM FLOW-SHOP SCHEDULING, MINIMUM JOB SHOP SCHEDULING)

467
Wöginger, G. J., and Yu, Z. (1992),
``A heuristic for preemptive scheduling with set-up times'',
Computing 49, 151-158.
(MINIMUM PREEMPTIVE SCHEDULING WITH SET-UP TIMES)

468
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``Exact and approximation algorithms for constructing ultrametric trees from distance metrics'',
Proc. 4th Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci. 1449, Springer-Verlag, 299-308.
(MINIMUM SIZE ULTRAMETRIC TREE)

469
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``A polynomial time approximation scheme for Minimum routing cost spanning tree'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 21-32.
(MINIMUM COMMUNICATION COST SPANNING TREE, MINIMUM TREE ALIGNMENT)

470
Yannakakis, M. (1979),
``The effect of a connectivity requirement on the complexity of maximum subgraph problems'',
J. ACM 26, 618-630.
(MINIMUM VERTEX DELETION TO OBTAIN CONNECTED SUBGRAPH WITH PROPERTY P)

471
Yannakakis, M., and Gavril, F. (1980),
``Edge dominating sets in graphs'',
SIAM J. Appl. Math. 38, 364-372.
(MINIMUM MAXIMAL MATCHING)

472
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``A .699 approximation algorithm for Max-Bisection'',
Math. Programming , to appear.
http://dollar.biz.uiowa.edu/col/ye/
(MAXIMUM CUT)

473
Yu, B., and Cheriyan, J. (1995),
``Approximation algorithms for feasible cut and multicut problems'',
Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 394-408.
(MINIMUM MULTI-CUT)

474
Yue, M. (1991),
``A simple proof of the inequality $MFFD(L)\le
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Technical Report RRR # 20-91, Rutcor, Rutgers Center for Operations Research, Rutgers University, New Jersey.
(MINIMUM BIN PACKING)

475
Zhang, K., and Jiang, T. (1994),
``Some MAX SNP-hard results concerning unordered labeled trees'',
Inform. Process. Lett. 49, 249-254.
(MAXIMUM COMMON EMBEDDED SUB-TREE)

476
Zuckerman, D. (1993),
``NP-complete problems have a version that's hard to approximate'',
Proc. Eight Ann. Structure in Complexity Theory Conf., IEEE Computer Society, 305-312.
(MINIMUM VERTEX COVER, MINIMUM GRAPH COLORING, MINIMUM FEEDBACK VERTEX SET, MINIMUM FEEDBACK ARC SET, MINIMUM CLIQUE COVER, MINIMUM STEINER TREE, MAXIMUM K-CUT, MAXIMUM 3-DIMENSIONAL MATCHING, MINIMUM SET COVER, MINIMUM HITTING SET, MAXIMUM CONSTRAINED PARTITION, MAXIMUM CONSTRAINED SEQUENCING TO MINIMIZE TARDY TASK WEIGHT)

477
Zwick, U. (1998),
``Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint'',
Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 201.
(MAXIMUM NOT-ALL-EQUAL 3-SATISFIABILITY, MAXIMUM K-CONSTRAINT SATISFACTION)



Viggo Kann
2000-04-23