Algorithmics of Matching Under Preferences

Algorithmics of Matching Under Preferences

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Matching problems with preferences are all around us: they arise when agents seek to be allocated to one another on the basis of ranked preferences over potential outcomes. Efficient algorithms are needed for producing matchings that optimise the satisfaction of the agents according to their preference lists. In recent years there has been a sharp increase in the study of algorithmic aspects of matching problems with preferences, partly reflecting the growing number of applications of these problems worldwide. The importance of the research area was recognised in 2012 through the award of the Nobel Prize in Economic Sciences to Alvin Roth and Lloyd Shapley. This book describes the most important results in this area, providing a timely update to The Stable Marriage Problem: Structure and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in connection with stable matching problems, whilst also broadening the scope to include matching problems with preferences under a range of alternative optimality criteria. Contents:Preliminary Definitions, Results and MotivationStable Matching Problems:The Stable Marriage Problem: An UpdateSM and HR with IndifferenceThe Stable Roommates ProblemFurther Stable Matching ProblemsOther Optimal Matching Problems:Pareto Optimal MatchingsPopular MatchingsProfile-Based Optimal Matchings Readership: Students and Professionals interested in algorithms, especially in the study of algorithmic aspects of matching problems with preferences. Keywords:Matching Problems;Preferences;Algorithms;Stable Marriage Problem;Hospitals / Residents Problem;House Allocation Problem;Stable Roomates ProblemKey Features:Provides a much-needed a€œsequela€ to Gusfield and Irving, given that so many papers on matching problems with preferences have been published since 1989Collects together a survey of the main results from these publications in a single volumeContains unique single survey on efficient algorithms for constructing optimal matchings where the optimality criterion does not involve stabilityReviews: a€œBesides being extremely useful to those who are interested in design and analysis techniques related to algorithms and complexity issues related to the matching of agents to one another when preferences are involved, involved readers can also benefit from the easy way it presents various ideas and approaches to problem solutions. It is written in a highly scientific language and it is extraordinarily beneficial reading for post-docs and researchers in mathematics and in game theory that focus on algorithms for solving matching problems and also study applications involving such problems.a€ Zentralblatt MATHGale-Shapley stable marriage problem revisited: strategic issues and applications, Management Science 47, 9, pp. ... Cited on page(s): 73 van Hentenryck, P., Deville, Y. and Teng, C-M. ... Majority voting in stable marriage problem with couples, in Proceedings of ICEIS a#39;04: the 6th International Conference on Enterpriseanbsp;...

Title:Algorithmics of Matching Under Preferences
Author: David F Manlove
Publisher:World Scientific - 2013-03-20

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