Abstract
We consider the problem of choosing the best matching of people to positions based on preferences expressed by the people, for which many different optimality criteria have been proposed. A matching is popular if no other matching beats it in a majority vote of the people. The popularity criterion has a manipulation-resistance property, but unfortunately, some sets of preferences admit no popular matching. In this paper, we introduce the least-unpopularity-factor and least-unpopularity-margin criteria, two generalizations of popularity that preserve the manipulation-resistance property but give an optimal matching for every set of preferences. Under each of these generalizations, we show that the “badness” of a given matching can be calculated efficiently but it is NP-hard to find an optimal matching.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abraham, D., Cechlárová, K., Manlove, D., Mehlhorn, K.: Pareto Optimality in House Allocation Problems. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 3–15. Springer, Heidelberg (2004)
Abraham, D., Irving, R., Kavitha, T., Mehlhorn, K.: Popular matchings. In: Proceedings of SODA 2005: The 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 424–432 (2005)
Abraham, D., Kavitha, T.: Dynamic matching markets and voting paths. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 65–76. Springer, Heidelberg (2006)
Gale, D., Shapley, L.: College admissions and the stability of marriage. American Mathematical Monthly 16, 9–15 (1962)
Gärdenfors, P.: Match Making: assignments based on bilateral preferences. Behavioural Sciences 20, 166–173 (1975)
Goldberg, A.: Scaling algorithms for the shortest paths problem. In: Proceedings of SODA 1993: The 4th ACM-SIAM Symposium on Discrete Algorithms, pp. 222–231 (1993)
Irving, R., Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: Rank-maximal matchings. In: Proceedings of SODA 2004: the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 68–75 (2004)
Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity, ch. 11. In: Weighted Matching. Prentice-Hall, Englewood Cliffs (1982)
Price, E.: Personal communication (August 2005)
Roth, A.: The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy 92, 991–1016 (1984)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McCutchen, R.M. (2008). The Least-Unpopularity-Factor and Least-Unpopularity-Margin Criteria for Matching Problems with One-Sided Preferences. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_51
Download citation
DOI: https://doi.org/10.1007/978-3-540-78773-0_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78772-3
Online ISBN: 978-3-540-78773-0
eBook Packages: Computer ScienceComputer Science (R0)