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** Index**

- INSTANCE:
Collection
*C* of finite sets.
- SOLUTION:
A set packing, i.e., a collection of disjoint sets .
- MEASURE:
Cardinality of the set packing, i.e., .

*Good News:*
See MAXIMUM CLIQUE.
*Bad News:*
See MAXIMUM CLIQUE.
*Comment:*
Also called *Maximum Hypergraph Matching*.
Equivalent to MAXIMUM CLIQUE under PTAS-reduction, where
[46]. Therefore approximation algorithms and
nonapproximability results (in terms of )
for MAXIMUM CLIQUE will carry over to
MAXIMUM SET PACKING.
In the weighted version of the problem the sets have positive weights and
the objective is to maximize the total weight of the sets in the set packing.
The equivalence to MAXIMUM CLIQUE holds also in the weighted case.
Approximable within ,
where *S* is the
underlying base set [229]. This holds also in the weighted
case [224].
The problem MAXIMUM *K*-SET PACKING, the variation in which the cardinality of
all sets in *C* are bounded from above by a constant ,
is APX-complete [280], and is approximable within
for any
[265].
The weighted version is approximable
within
for any
[30] and within
*2(k+1)/3* [98].
If the number of occurrences in *C* of
any element is bounded by a constant *B* for
the problem is APX-complete [75] and
approximable within *B*, even for the weighted variation of
the problem [248].
*Garey and Johnson:* SP3

** Next:** MAXIMUM SET SPLITTING
** Up:** Covering, Hitting, and Splitting
** Previous:** MAXIMUM 3-DIMENSIONAL MATCHING
** Index**
*Viggo Kann*

*2000-03-20*