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

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Taneli Mielikäinen, Esko Ukkonen
• Keywords: DAM 2006, Maximum Intersection Problem, Maximum Matroid-matroid Intersection, NP-hard