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International Symposium on Mathematical Foundations of Computer Science

MFCS 2014: Mathematical Foundations of Computer Science 2014 pp 625–636Cite as

Approximation Algorithms for Bounded Color Matchings via Convex Decompositions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

We study the following generalization of the maximum matching problem in general graphs: Given a simple non-directed graph G = (V,E) and a partition of the edges into k classes (i.e. E = E 1 ∪ ⋯ ∪ E k ), we would like to compute a matching M on G of maximum cardinality or profit, such that |M ∩ E j | ≤ w j for every class E j . Such problems were first studied in the context of network design in [17]. We study the problem from a linear programming point of view: We provide a polynomial time \(\frac{1}{2}\)-approximation algorithm for the weighted case, matching the integrality gap of the natural LP formulation of the problem. For this, we use and adapt the technique of approximate convex decompositions [19] together with a different analysis and a polyhedral characterization of the natural linear program to derive our result. This improves over the existing \(\frac{1}{2}\), but with additive violation of the color bounds, approximation algorithm [14].

Part of this work was done while the author was a PhD student at IDSIA.

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Author information

Authors and Affiliations

  1. LAMSADE, CNRS UMR 7243, Universitè Paris-Dauphine, France

    Georgios Stamoulis

  2. Universitá della Svizzera Italiana (USI), Lugano, Switzerland

    Georgios Stamoulis

Authors
  1. Georgios Stamoulis
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Stamoulis, G. (2014). Approximation Algorithms for Bounded Color Matchings via Convex Decompositions. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_53

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  • DOI: https://doi.org/10.1007/978-3-662-44465-8_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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