Set Packing
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High Quality Content by WIKIPEDIA articles! Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose we have a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them intersect). The problem is clearly in NP since, given k subsets, we can easily verify that they are pairwise disjoint. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint ...
High Quality Content by WIKIPEDIA articles! Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose we have a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them intersect). The problem is clearly in NP since, given k subsets, we can easily verify that they are pairwise disjoint. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list. It is a maximization problem that can be formulated naturally as an integer linear program, belongs to the class of packing problems, and its dual linear program is the set cover problem.
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