An improved approximation lower bound for finding almost stable maximum matchings

Authors:
Koki Hamada;Kazuo Iwama;Shuichi Miyazaki
Affiliations:
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan;Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan;Academic Center for Computing and Media Studies, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Venue:
Information Processing Letters
Year:
2009

Citing 2
Cited 3

The stable marriage problem: structure and algorithms

The stable marriage problem: structure and algorithms
“Almost stable” matchings in the roommates problem

WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms

Size versus stability in the marriage problem

Theoretical Computer Science
The hospitals/residents problem with quota lower bounds

ESA'11 Proceedings of the 19th European conference on Algorithms
“Almost stable” matchings in the Roommates problem with bounded preference lists

Theoretical Computer Science

Quantified Score

Hi-index	0.89

Visualization

Abstract

In the stable marriage problem that allows incomplete preference lists, all stable matchings for a given instance have the same size. However, if we ignore the stability, there can be larger matchings. Biro et al. defined the problem of finding a maximum cardinality matching that contains minimum number of blocking pairs. They proved that this problem is not approximable within some constant @d1 unless P=NP, even when all preference lists are of length at most 3. In this paper, we improve this constant @d to n^1^-^@e for any @e0, where n is the number of men in an input.