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Size Versus Stability in the Marriage Problem

  • Péter Biró
  • David F. Manlove
  • Shubham Mittal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5426)

Abstract

Given an instance I of the classical Stable Marriage problem with Incomplete preference lists (smi), a maximum cardinality matching can be larger than a stable matching. In many large-scale applications of smi, we seek to match as many agents as possible. This motivates the problem of finding a maximum cardinality matching in I that admits the smallest number of blocking pairs (so is “as stable as possible”). We show that this problem is NP-hard and not approximable within n 1 − ε , for any ε> 0, unless P=NP, where n is the number of men in I. Further, even if all preference lists are of length at most 3, we show that the problem remains NP-hard and not approximable within δ, for some δ> 1. By contrast, we give a polynomial-time algorithm for the case where the preference lists of one sex are of length at most 2.

Keywords

Perfect Match Vertex Cover Maximum Match Stable Match Preference List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Péter Biró
    • 1
  • David F. Manlove
    • 1
  • Shubham Mittal
    • 2
  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK
  2. 2.Department of Computer Science and Engineering, Block VIIndian Institute of Technology, Delhi, Hauz KhasNew DelhiIndia

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