Improved approximation results for the stable marriage problem

Magnús M. Halldórsson*, Kazuo Iwama, Shuichi Miyazaki, Hiroki Yanagisawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)


The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm. In this article, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of 2/(1 + L -2) for instances in which only men have ties of length at most L. When both men and women are allowed to have ties but the lengths are limited to two, then we show a ratio of 13/7(<1.858). We also improve the lower bound on the approximation ratio to 21/19(>1.1052).

Original languageEnglish
Article number1273346
JournalACM Transactions on Algorithms
Issue number3
Publication statusPublished - 1 Aug 2007

Other keywords

  • Approximation algorithms
  • Incomplete lists
  • Stable marriage problem
  • Ties


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