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Set Packing Problem


A set packing in a collection C of finite sets is a subcollection P subset= C such that any two members are disjoint sets. The set packing problem asks whether C contains a set packing with at least k members. It is NP-complete (Karp 1972).

Set packing generalizes the independent set problem: associate a graph vertex with each member of C and join two graph vertices when the corresponding sets intersect. Set packings then correspond exactly to independent sets in the resulting intersection graph.


See also

Independent Set, Set Cover Problem, Set Partition

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References

Karp, R. M. "Reducibility Among Combinatorial Problems." In Complexity of Computer Computations, Proc. Sympos. IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972 (Ed. R. E. Miller and J. W. Thatcher). New York: Plenum, pp. 85-103, 1972. https://doi.org/10.1007/978-1-4684-2001-2_9.

Cite this as:

Weisstein, Eric W. "Set Packing Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SetPackingProblem.html

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