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A Polyhedral Approach to Online Bipartite Matching

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

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Abstract

We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of an underlying distribution, and must immediately be matched or discarded. We consider various relaxations of the set of achievable matching probabilities, introduce star inequalities and their generalizations, and discuss when they are facet-defining. We also show how several of these relaxations correspond to ranking policies and their time-dependent generalizations. We finally present results of a computational study of these relaxations and policies to determine their empirical performance.

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Authors and Affiliations

  1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332, Atlanta, Georgia

    Alfredo Torrico, Shabbir Ahmed & Alejandro Toriello

Authors
  1. Alfredo Torrico
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  2. Shabbir Ahmed
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  3. Alejandro Toriello
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Corresponding author

Correspondence to Alejandro Toriello .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Torrico, A., Ahmed, S., Toriello, A. (2016). A Polyhedral Approach to Online Bipartite Matching. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_24

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33460-8

  • Online ISBN: 978-3-319-33461-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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