Representative families for matroid intersections, with applications to location, packing, and covering problems

TL;DR

This paper develops algorithms for computing representative families in matroid intersections and applies them to fixed-parameter algorithms for problems like set packing, covering, and facility location, highlighting both tractability and hardness results.

Contribution

It introduces algorithms for representative families in matroid intersections and applies them to solve complex combinatorial problems with multiple constraints.

Findings

Algorithms for representative families in matroid intersections.

Fixed-parameter algorithms for set packing, covering, and facility location.

Hardness results complementing tractability findings.

Abstract

We show algorithms for computing representative families for matroid intersections and use them in fixed-parameter algorithms for set packing, set covering, and facility location problems with multiple matroid constraints. We complement our tractability results by hardness results.