Algorithmics of Matching Under Preferences

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 Motivation

• Stable Matching Problems:

  • The Stable Marriage Problem: An Update
  • SM and HR with Indifference
  • The Stable Roommates Problem
  • Further Stable Matching Problems

• Other Optimal Matching Problems:

  • Pareto Optimal Matchings
  • Popular Matchings
  • Profile-Based Optimal Matchings

Readership: Students and Professionals interested in algorithms, especially in the study of algorithmic aspects of matching problems with preferences.
Key Features:

• Provides a much-needed “sequel” to Gusfield and Irving, given that so many papers on matching problems with preferences have been published since 1989
• Collects together a survey of the main results from these publications in a single volume
• Contains unique single survey on efficient algorithms for constructing optimal matchings where the optimality criterion does not involve stability