Facility location under matroid constraints: fixed-parameter algorithms and applications
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We study an NP-hard uncapacitated discrete facility location problem: The task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids. Combining the color coding technique with representative sets of matroid intersections, we show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids. We apply this algorithm to obtain fixed-parameter algorithms for social network analysis, line planning in public transport, and team management. We complement our tractability results by lower bounds.
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