Algorithmics of matching under preferences

by Manlove, David F.

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :Algorithmics of matching under preferences / by David Manlove, University of Glasgow, UK ; with a foreword by Kurt Mehlhorn.

Summary

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. 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.

Edition Statements

Publication Date:©2013

Publication Statements

Publisher(s):World Scientific
Place of Publication:Hackensack, New Jersey
Language:eng
Publication Date:©2013

The Physical Object

Description:1 online resource (xxxi, 415 pages).

Edition Identifiers

ISBN:9789814425254, 9814425257
oclc:ocn840497867
LC Classification:QA164
Dewey Decimal:511.66

1. Preliminary definitions, results and motivation. 1.1. Introduction. 1.2. Matchings in graphs. 1.3. The Hospitals / Residents problem (HR). 1.4. The Stable Roommates problem (SR). 1.5. The House Allocation problem (HA) and its variants -- 2. The Stable Marriage problem: an update. 2.1. Introduction. 2.2. The 12 open problems of Gusfield and Irving. 2.3. The Subramanian and Feder papers. 2.4. Linear programming approaches. 2.5. Constraint programming approaches. 2.6. Paths to stability. 2.7. Median stable matchings. 2.8. Size versus stability. 2.9. Strategic issues. 2.10. Further results. 2.11. Conclusions and open problems -- 3. SM and HR with indifference. 3.1. Introduction. 3.2. Weak stability. 3.3. Strong stability. 3.4. Super-stability. 3.5. Other results. 3.6. Conclusions and open problems -- 4. The Stable Roommates problem. 4.1. Introduction. 4.2. Updates to open problems 8-12 from Gusfield & Irving. 4.3. Stable partitions. 4.4. Mirror posets and median graphs. 4.5. Indifference. 4.6. "Almost stable" matchings. 4.7. Globally-ranked pairs. 4.8. Other extensions of SR. 4.9. Conclusions and open problems -- 5. Further stable matching problems. 5.1. Introduction. 5.2. HR with …