The Complexity of Maximum Matroid-Greedoid Intersection

Abstract. The maximum intersection problem for a matroid and a greedoid, given by polynomial-time oracles, is shown NP-hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. Also the corresponding approximation problem is shown NP-hard for certain approximation performance bounds. This is in contrast with the maximum matroid-matroid intersection which is solvable in polynomial time by an old result of Edmonds.

• Type: Conference
• Year: 2001
• Where: FCT
• Authors: Taneli Mielikäinen, Esko Ukkonen
• Keywords: Applied Computing, Corresponding Approximation Problem, FCT 2001, Maximum Intersection Problem, Maximum Matroid-matroid Intersection