A (k+3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems

Ward, Justin

doi:10.4230/LIPIcs.STACS.2012.42

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A (k+3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems

Author Justin Ward

Part of: Volume: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-02-24

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LIPIcs.STACS.2012.42.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2012.42
URN: urn:nbn:de:0030-drops-34315

Subject Classification

Keywords

k-set packing
k-exchange systems
submodular maximization
local search
approximation algorithms

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Abstract

We consider the monotone submodular k-set packing problem in the context of the more general problem of maximizing a monotone submodular function in a k-exchange system. These systems, introduced by Feldman et al. [Feldman,2011], generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization problems.  We give a deterministic, non-oblivious local search algorithm that attains an approximation ratio of (k + 3)/2 + epsilon for the problem of maximizing a monotone submodular function in a k-exchange system, improving on the best known result of k+epsilon, and answering an open question posed by Feldman et al.

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Justin Ward. A (k+3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 42-53, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.STACS.2012.42

Author Details

Justin Ward

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