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Adapting stable matchings to forced and forbidden pairs

Published: 01 February 2025 Publication History

Abstract

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching M 1, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to M 1. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable.

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Published In

cover image Journal of Computer and System Sciences
Journal of Computer and System Sciences  Volume 147, Issue C
Feb 2025
94 pages

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 February 2025

Author Tags

  1. Stable Marriage
  2. Stable Roommates
  3. Forced and forbidden pairs
  4. Incremental algorithms
  5. Rotations
  6. NP-hardness
  7. Polynomial-time algorithm
  8. W[1]-hardness
  9. FPT

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