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Fractional Matching Via Balls-and-Bins

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2006, RANDOM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4110))

Abstract

We relate the problem of finding structures related to perfect matchings in bipartite graphs to a stochastic process similar to throwing balls into bins. We view each node on the left of a bipartite graph as having balls that it can throw into nodes on the right (bins) to which it is adjacent. We show that several simple algorithms based on throwing balls into bins deliver a near-perfect fractional matching, where a perfect fractional matching is a weighted subgraph on all nodes with nonnegative weights on edges so that the total weight incident at each node is 1.

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Author information

Authors and Affiliations

  1. Dept of Computer Science, Stanford University,  

    Rajeev Motwani, Rina Panigrahy & Ying Xu

Authors
  1. Rajeev Motwani
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  2. Rina Panigrahy
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  3. Ying Xu
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Battelle Bâtiment A, Route de Drize 7,, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Uri Zwick

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© 2006 Springer-Verlag Berlin Heidelberg

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Motwani, R., Panigrahy, R., Xu, Y. (2006). Fractional Matching Via Balls-and-Bins. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2006 2006. Lecture Notes in Computer Science, vol 4110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11830924_44

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  • DOI: https://doi.org/10.1007/11830924_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38044-3

  • Online ISBN: 978-3-540-38045-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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