Stable marriages with multiple partners: efficient search for an optimal solution

Authors:
Vipul Bansal;Aseem Agrawal;Varun S. Malhotra
Affiliations:
Adobe Systems, Noida, India;IBM India Research Lab., New Delhi, India;Stanford University, Electrical Engineering Dept., CA
Venue:
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Year:
2003

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Abstract

This paper considers the many-to-many version of the original stable marriage problem posed by Gale and Shapley [1]. Each man and woman has a strict preference ordering on the members of the opposite sex and wishes to be matched with upto his or her specified number of partners. In this setup, a polynomial time algorithm for finding a stable matching that minimizes the sum of partner ranks across all men and women is provided. It is argued that this sum can be used as an optimality criterion for minimizing total dissatisfaction if the preferences over partner-combinations satisfy a no-complementarities condition. The results in this paper extend those already known for the one-to-one version of the problem.