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The Stable Roommates problem with short lists

Author

Listed:
  • Agnes Cseh

    (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest)

  • Robert W. Irving

    (School of Computing Science, University of Glasgow)

  • David F. Manlove

    (School of Computing Science, Sir Alwyn Williams Building, University of Glasgow)

Abstract

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length. The first variant, egal d-sri, involves finding an egalitarian stable matching in solvable instances of sri with preference lists of length at most d. We show that this problem is NP-hard even if d = 3. On the positive side we give a 2d+3 7 -approximation algorithm for d 2 {3, 4, 5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of sri, called d-srti, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-srti admits a stable matching is NP-complete even if d = 3. We also consider the “most stable” version of this problem and prove a strong inapproximability bound for the d = 3 case. However for d = 2 we show that the latter problem can be solved in polynomial time.

Suggested Citation

  • Agnes Cseh & Robert W. Irving & David F. Manlove, 2017. "The Stable Roommates problem with short lists," CERS-IE WORKING PAPERS 1726, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1726
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    References listed on IDEAS

    as
    1. Chung-Piaw Teo & Jay Sethuraman, 1998. "The Geometry of Fractional Stable Matchings and Its Applications," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 874-891, November.
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    More about this item

    Keywords

    stable matching; bounded length preference lists; complexity; approximation algorithm;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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