Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints
We consider an uncapacitated discrete facility location problem where 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. We show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids. To this end, we derive fixed-parameter algorithms for computing representative families for matroid intersections and maximum-weight set packings with multiple matroid constraints. To illustrate the modeling capabilities of the new problem, we use it to obtain algorithms for a problem in social network analysis. We complement our tractability results by lower bounds.
KeywordsMatroid set packing Matroid parity Matroid median Representative families Social network analysis Strong triadic closure
This study was initiated at the 7th annual research retreat of the Algorithmics and Computational Complexity group of TU Berlin, Darlingerode, Germany, March 18th–23rd, 2018. R. van Bevern and O. Yu. Tsidulko were supported by the Russian Foundation for Basic Research, grants 16-31-60007 mol_a_dk and 18-31-00470 mol_a, respectively. Both were supported by Russian Science Foundation grant 16-11-10041 while working on Sect. 3.
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