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Online total bipartite matching problem

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Abstract

This paper analyzes a variant of Online Bipartite Matching in which incoming jobs must be matched to some worker, even if there are no available edges. A reward is only gained for matchings that are made across some edge. This paper gives matching upper and lower bounds for the most general version of this variation. It then provides an optimal policy for this problem when the underlying bipartite graph meets certain conditions and then identifies the most general conditions under which this policy is guaranteed to be optimal.

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Acknowledgements

This research was supported in part by the Air Force Office of Scientific Research (FA9550-19-1-0106). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force, Department of Defense, or the United States Government.

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  1. Department of Computer Science, University of Illinois Urbana-Champaign, Champaign, USA

    Meghan Shanks & Sheldon H. Jacobson

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  1. Meghan Shanks
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  2. Sheldon H. Jacobson
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Correspondence to Meghan Shanks.

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Shanks, M., Jacobson, S.H. Online total bipartite matching problem. Optim Lett 16, 1411–1426 (2022). https://doi.org/10.1007/s11590-021-01814-0

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