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A polyhedral approach to online bipartite matching

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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 a uniform distribution, and must immediately be matched or discarded. We consider various relaxations of the polyhedral set of achievable matching probabilities, introduce valid inequalities, 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 a computational study of these relaxations and policies to determine their empirical performance.

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Acknowledgements

A. Torrico and A. Toriello were partially supported by the National Science Foundation via grant CMMI-1552479.

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Authors and Affiliations

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

    Alfredo Torrico, Shabbir Ahmed & Alejandro Toriello

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  1. Alfredo Torrico
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  2. Shabbir Ahmed
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  3. Alejandro Toriello
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Correspondence to Alejandro Toriello.

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Torrico, A., Ahmed, S. & Toriello, A. A polyhedral approach to online bipartite matching. Math. Program. 172, 443–465 (2018). https://doi.org/10.1007/s10107-017-1219-3

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  • DOI: https://doi.org/10.1007/s10107-017-1219-3

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