TY - GEN

T1 - On the (parameterized) complexity of almost stable marriage

AU - Gupta, Sushmita

AU - Jain, Pallavi

AU - Roy, Sanjukta

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© Sushmita Gupta, Pallavi Jain, Sanjukta Roy, Saket Saurabh, and Meirav Zehavi; licensed under Creative Commons License CC-BY.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the “no blocking pair” condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, the goal is to find a matching whose size exceeds that of a stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k, t, d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k + t + d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is “closest”, in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm.

AB - In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the “no blocking pair” condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, the goal is to find a matching whose size exceeds that of a stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k, t, d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k + t + d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is “closest”, in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm.

KW - Local Search

KW - Parameterized Complexity

KW - Stable Matching

UR - http://www.scopus.com/inward/record.url?scp=85101490985&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2020.24

DO - 10.4230/LIPIcs.FSTTCS.2020.24

M3 - Conference contribution

AN - SCOPUS:85101490985

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2020

A2 - Saxena, Nitin

A2 - Simon, Sunil

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2020

Y2 - 14 December 2020 through 18 December 2020

ER -