Chapter

Automata, Languages and Programming

Volume 1644 of the series Lecture Notes in Computer Science pp 443-452

Date:

Stable Marriage with Incomplete Lists and Ties

  • Kazuo IwamaAffiliated withSchool of Informatics, Kyoto University
  • , Shuichi MiyazakiAffiliated withSchool of Informatics, Kyoto University
  • , Yasufumi MoritaAffiliated withSchool of Informatics, Kyoto University
  • , David ManloveAffiliated withDept. of Computing Science, University of Glasgow

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Abstract

The original stable marriage problem requires all men and women to submit a complete and strictly ordered preference list. This is obviously often unrealistic in practice, and several relaxations have been proposed, including the following two common ones: one is to allow an incomplete list, i.e., a man is permitted to accept only a subset of the women and vice versa. The other is to allow a preference list including ties. Fortunately, it is known that both relaxed problems can still be solved in polynomial time. In this paper, we show that the situation changes substantially if we allow both relaxations (incomplete lists and ties) at the same time: the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N 1- , where N is the instance size, unless P=NP.