The Complexity of Maximum Matroid-Greedoid Intersection and Weighted Greedoid Maximization

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. 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. … Read more