The Stable Roommates Problem with Short Lists

  • Ágnes CsehEmail author
  • Robert W. Irving
  • David F. Manlove
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9928)


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 \(\textsf {NP}\)-hard even if \(d=3\). On the positive side we give a \(\frac{2d+3}{7}\)-approximation algorithm for \(d\in \{3,4,5\}\) 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 \(\textsf {NP}\)-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.


Approximation Algorithm Match History Stable Match Preference List Minimum Vertex Cover 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ágnes Cseh
    • 1
    Email author
  • Robert W. Irving
    • 2
  • David F. Manlove
    • 2
  1. 1.School of Computer ScienceReykjavik UniversityReykjavíkIceland
  2. 2.School of Computing ScienceUniversity of GlasgowGlasgowScotland, UK

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