The stable roommates problem with ties

We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear–time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2

A Sublinear Parallel Algorithm for Stable Matching

. Parallel algorithms for various versions of the stable matching problem are presented. The algorithms are based on the primal-dual interior pathfollowing method for linear programming. The main result is that a stable matching can be found in O ( p m) time by a polynomial number of processors, where m is the total length of preference lists of individuals. 1. Introduction In this paper we consider networks made of gates of constant size. We focus of nonexpansive networks (to be defined below). The problems of evaluating the gate to which a network converges, and of finding a stable configuration in a network, are quite simple in the context of sequential computation; they can all be solved in linear time in the scatter-free case (a special case, Mayr and Subramanian [5]), and in quadratic time in the general nonexpansive case (Feder [1]). An interesting question is the existence of sublinear parallel algorithms with a polynomial number of processors. We present parallel algorith..

A sublinear parallel algorithm for stable matching

A parallel algorithm for the stable matching problem is presented. The algorithm is based on the primal-dual interior path-following method for linear programming. The main result is that a stable matching can be found in 0*(Jiii) time by a polynomial number of processors, where nz is the total length of preference lists of individuals. @ 2000 Published by Elsevier Sciencc B.V. All rights reserved. Keywords: Non-expansive circuits; Linear programming; Stable matchin