Better and Simpler Approximation Algorithms for the Stable Marriage Problem

  • Zoltán Király
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

Abstract

We first consider the problem of finding a maximum stable matching if incomplete lists and ties are both allowed, but ties only for one gender. 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 [7]. 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.

Keywords

stable matching Hospitals/Residents problem approximation algorithms 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zoltán Király
    • 1
  1. 1.Department of Computer Science and Communication Networks LaboratoryEötvös University, Pázmány Péter sétány 1/CBudapestHungary

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