TY - GEN

T1 - The price of matching with metric preferences

AU - Emek, Yuval

AU - Langner, Tobias

AU - Wattenhofer, Roger

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

PY - 2015

Y1 - 2015

N2 - We consider a version of the Gale-Shapley stable matching setting, where each pair of nodes is associated with a (symmetric) matching cost and the preferences are determined with respect to these costs. This stable matching version is analyzed through the Price of Anarchy (PoA) and Price of Stability (PoS) lens under the objective of minimizing the total cost of matched nodes (for both the marriage and roommates variants). A simple example demonstrates that in the general case, the PoA and PoS are unbounded, hence we restrict our attention to metric costs. We use the notion of α-stability, where a pair of unmatched nodes defect only if both improve their costs by a factor greater than α ≥ 1. Our main result is an asymptotically tight trade-off, showing that with respect to α-stable matchings, the Price of Stability is [Formula presented]. The proof is constructive: we present a simple algorithm that outputs an α-stable matching satisfying this bound.

AB - We consider a version of the Gale-Shapley stable matching setting, where each pair of nodes is associated with a (symmetric) matching cost and the preferences are determined with respect to these costs. This stable matching version is analyzed through the Price of Anarchy (PoA) and Price of Stability (PoS) lens under the objective of minimizing the total cost of matched nodes (for both the marriage and roommates variants). A simple example demonstrates that in the general case, the PoA and PoS are unbounded, hence we restrict our attention to metric costs. We use the notion of α-stability, where a pair of unmatched nodes defect only if both improve their costs by a factor greater than α ≥ 1. Our main result is an asymptotically tight trade-off, showing that with respect to α-stable matchings, the Price of Stability is [Formula presented]. The proof is constructive: we present a simple algorithm that outputs an α-stable matching satisfying this bound.

UR - http://www.scopus.com/inward/record.url?scp=84945558758&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48350-3_39

DO - 10.1007/978-3-662-48350-3_39

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AN - SCOPUS:84945558758

SN - 9783662483497

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 459

EP - 470

BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings

A2 - Bansal, Nikhil

A2 - Finocchi, Irene

T2 - 23rd European Symposium on Algorithms, ESA 2015

Y2 - 14 September 2015 through 16 September 2015

ER -