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Finding all stable matchings with assignment constraints

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  • Gregory Gutin
  • Philip R. Neary
  • Anders Yeo

Abstract

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives, that determines if assignment constraints are compatible with stability. Whenever there is a stable matching that satisfies the assignment constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.

Suggested Citation

  • Gregory Gutin & Philip R. Neary & Anders Yeo, 2022. "Finding all stable matchings with assignment constraints," Papers 2204.03989, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2204.03989
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    References listed on IDEAS

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    Cited by:

    1. Gregory Z. Gutin & Daniel Karapetyan & Philip R. Neary & Alexander Vickery & Anders Yeo, 2024. "Speeding up deferred acceptance," Papers 2409.06865, arXiv.org.

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