Better and simpler approximation algorithms for the stable marriage problem

Zoltán Király

Published in:
Algorithms - ESA 2008, Lecture Notes in Computer Science Volume 5193, 2008, pp 623-634


We first consider the problem of finding a maximum size stable matching if incomplete lists and ties are both allowed, but ties are on one side only. For this problem we give a simple, linear time 3/2-approximation algorithm, improving on the best known approximation factor 5/3 of Irving and Manlove [5]. Next, we show how this extends to the Hospitals/Residents problem with the same ratio if the residents have strict orders. We also give a simple linear time algorithm for the general problem with approximation factor 5/3, improving the best known 15/8-approximation algorithm of Iwama, Miyazaki and Yamauchi [8]. For the cases considered in this paper it is NP-hard to approximate within a factor of 21/19 by the result of Halldórsson et al. [3].
Our algorithms not only give better approximation ratios than the cited ones, but are much simpler and run significantly faster. Also we may drop a restriction used in [5] and the analysis is substantially more moderate.
Preliminary versions of this paper appeared in [9, 10, 11]. For the related results obtained thenceforth see Section 5.

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Bibtex entry:

AUTHOR = {Kir{\'a}ly, Zolt{\'a}n},
TITLE = {Better and simpler approximation algorithms for the stable marriage problem},
NOTE= {{\tt}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2008},
NUMBER = {TR-2008-04}

Last modification: 10.9.2021. Please email your comments to Tamás Király!