Pareto optimality in house allocation problems

Authors:
David J. Abraham;Katarína Cechlárová;David F. Manlove;Kurt Mehlhorn
Affiliations:
Computer Science Department, Carnegie-Mellon University, Pittsburgh, PA;Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Košice, Slovakia;Department of Computing Science, University of Glasgow, Glasgow, UK;Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

Citing 5
Cited 4

Faster scaling algorithms for network problems

SIAM Journal on Computing
Minimum edge dominating sets

SIAM Journal on Discrete Mathematics
The complexity of economic equilibria for house allocation markets

Information Processing Letters
On the complexity of price equilibria

Journal of Computer and System Sciences - STOC 2002
Rank-maximal matchings

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

Reducing rank-maximal to maximum weight matching

Theoretical Computer Science
A fair assignment algorithm for multiple preference queries

Proceedings of the VLDB Endowment
Optimal partitions in additively separable hedonic games

IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Computing desirable partitions in additively separable hedonic games

Artificial Intelligence

Quantified Score

Hi-index	0.01

Visualization

Abstract

We study Pareto optimal matchings in the context of house allocation problems. We present an $O(\sqrt{n}m)$ algorithm, based on Gale's Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching.