On solution concepts for matching games

Biro, P., Kern, W., and Paulusma, D. (2010) On solution concepts for matching games. Lecture Notes in Computer Science, 6108, pp. 117-127. (doi:10.1007/978-3-642-13562-0_12)

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Publisher's URL: http://dx.doi.org/10.1007/978-3-642-13562-0_12

Abstract

A matching game is a cooperative game (N,v) defined on a graph G = (N,E) with an edge weighting w:E→R+ . The player set is N and the value of a coalition S ⊆ N is defined as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm + n 2logn) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and that computes a core allocation if the core is nonempty. This improves previous work based on the ellipsoid method. Second we show that the nucleolus of an n-player matching game with nonempty core can be computed in O(n 4) time. This generalizes the corresponding result of Solymosi and Raghavan for assignment games. Third we show that determining an imputation with minimum number of blocking pairs is an NP-hard problem, even for matching games with unit edge weights.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Biro, Dr Peter
Authors: Biro, P., Kern, W.,, and Paulusma, D.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:0302-9743

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE