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Popular matchings with weighted voters

Author

Listed:
  • Heeger, Klaus
  • Cseh, Ágnes

Abstract

We consider a natural generalization of the well-known Popular Matching problem where every vertex has a weight. We call a matching M more popular than matching M′ if the weight of vertices preferring M to M′ is larger than the weight of vertices preferring M′ to M. For this case, we show that it is NP-hard to find a popular matching. Our main result is a polynomial-time algorithm that delivers a popular matching or a proof for its non-existence in instances where all vertices on one side have weight c for some c>3 and all vertices on the other side have weight 1.

Suggested Citation

  • Heeger, Klaus & Cseh, Ágnes, 2024. "Popular matchings with weighted voters," Games and Economic Behavior, Elsevier, vol. 144(C), pages 300-328.
    • Handle: RePEc:eee:gamebe:v:144:y:2024:i:c:p:300-328
    DOI: 10.1016/j.geb.2024.01.015
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