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2006

The complexity of maximum matroid-greedoid intersection and weighted greedoid maximization,

11 years 5 months ago
The complexity of maximum matroid-greedoid intersection and weighted greedoid maximization,
The maximum intersection problem for a matroid and a greedoid, given by polynomialtime oracles, is shown NP-hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. The corresponding approximation problems are shown NP-hard for certain approximation performance bounds. Moreover, some natural parameterized variants of the problem are shown W[P]hard. The results are in contrast with the maximum matroid-matroid intersection which is solvable in polynomial time by an old result of Edmonds. We also prove that it is NP-hard to approximate the weighted greedoid maximization within 2nO(1) where n is the size of the domain of the greedoid. Key words: Combinatorial optimization, NP-hardness, Inapproximability, Fixed-parameter intractability
Taneli Mielikäinen, Esko Ukkonen
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DAM
Authors Taneli Mielikäinen, Esko Ukkonen
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