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Competitive Weighted Matching in Transversal Matroids

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Abstract

Consider a bipartite graph with a set of left-vertices and a set of right-vertices. All the edges adjacent to the same left-vertex have the same weight. We present an algorithm that, given the set of right-vertices and the number of left-vertices, processes a uniformly random permutation of the left-vertices, one left-vertex at a time. In processing a particular left-vertex, the algorithm either permanently matches the left-vertex to a thus-far unmatched right-vertex, or decides never to match the left-vertex. The weight of the matching returned by our algorithm is within a constant factor of that of a maximum weight matching, generalizing the recent results of Babaioff et al.

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Authors and Affiliations

  1. Operations Research Department, Naval Postgraduate School, 1411 Cunningham Rd., Monterey, CA, 93943, USA

    Nedialko B. Dimitrov

  2. Computer Science Department, The University of Texas at Austin, 1616 Guadalupe St., Austin, TX, 78701, USA

    C. Greg Plaxton

Authors
  1. Nedialko B. Dimitrov
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  2. C. Greg Plaxton
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Corresponding author

Correspondence to Nedialko B. Dimitrov.

Additional information

N.B. Dimitrov is supported by an MCD Fellowship from the University of Texas at Austin.

C.G. Plaxton is supported by NSF Grants CCF–0635203 and ANI–0326001.

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Dimitrov, N.B., Plaxton, C.G. Competitive Weighted Matching in Transversal Matroids. Algorithmica 62, 333–348 (2012). https://doi.org/10.1007/s00453-010-9457-2

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  • DOI: https://doi.org/10.1007/s00453-010-9457-2

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