Dimitrios Michail
Abstract
applicant provides a preference list, which may contain ties, ranking a subset of the posts. Different optimization criteria may be defined, which depend on the desired solution properties. The main focus of this work is to assess the quality of matchings computed by rank-maximal and popular matching algorithms and compare this with the minimum weight matching algorithm, which is a standard matching algorithm that is used in practice.
Both rank-maximal and popular matching algorithms use common algorithmic techniques, which makes them excellent candidates for a running time comparison. Since popular matchings do not always exist, we also study the unpopularity of matchings computed by the aforementioned algorithms. Finally, extra criteria like total weight and cardinality are included, due to their importance in practice. All experiments are performed using structured random instances as well as instances created using real-world datasets.
- Abraham, D. J., Irving, R. W., Kavitha, T., and Mehlhorn, K. 2007. Popular matchings. SIAM J. Comput. 37, 4, 1030--1045. Google Scholar
Digital Library
- Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. 1993. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs, NJ. Google ScholarDigital Library
- Bhatnagar, N., Greenberg, S., and Randall, D. 2008. Sampling stable marriages: Why spouse-swapping won't work. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'08). SIAM, Philadelphia, PA, 1223--1232. Google ScholarDigital Library
- Bogomolnaia, A. and Laslier, J.-F. 2007. Euclidean preferences. J. Math. Econ. 43, 2, 87--98.Google ScholarCross Ref
- Condorcet, M. J. 1785. Éssai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix.Google Scholar
- Gabow, H. N. and Tarjan, R. 1989. Faster scaling algorithms for network problems. SIAM J. Comput. 18, 1013--1036. Google ScholarDigital Library
- Gärdenfors, P. 1975. Match making: Assignments based on bilateral preferences. Behav. Sci. 20, 3, 166--173.Google ScholarCross Ref
- Goldberg, A. V. and Kennedy, R. 1995. An efficient cost scaling algorithm for the assignment problem. Math. Program. 71, 2, 153--177. Google ScholarDigital Library
- Graham, R. L., Grötschel, M., and Lovasz, L., Eds. 1995. The Handbook of Combinatorics. MIT Press, Cambridge, MA, 179--232. Google ScholarDigital Library
- Hopcroft, J. E. and Karp, R. M. 1973. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 4, 225--231.Google ScholarDigital Library
- Huang, C.-C., Kavitha, T., Michail, D., and Nasre, M. 2010. Bounded unpopularity matchings. Algorithmica, 1--20. 10.1007/s00453-010-9434-9. Google ScholarDigital Library
- Hylland, A. and Zeckhauser, R. 1979. The efficient allocation of individuals to positions. J. Political Econ. 87, 2, 293--314.Google ScholarCross Ref
- Irving, R. W., Kavitha, T., Mehlhorn, K., Michail, D., and Paluch, K. E. 2006. Rank-maximal matchings. ACM Trans. Algor. 2, 4, 602--610. Google ScholarDigital Library
- Kao, M.-Y., Lam, T. W., Sung, W.-K., and Ting, H.-F. 2001. A decomposition theorem for maximum weight bipartite matchings. SIAM J. Comput. 31, 1, 18--26. Google ScholarDigital Library
- Kavitha, T., Mestre, J., and Nasre, M. 2011. Popular mixed matchings. Theor. Comput. Sci. 412, 24, 2679--2690. Google ScholarDigital Library
- Langguth, J., Manne, F., and Sanders, P. 2010. Heuristic initialization for bipartite matching problems. J. Exp. Algorithmics 15, 1.3:1.1--1.3:1.22. Google ScholarDigital Library
- LIBMOSP 2010. Library for Matchings with One Sided Preferences. http://www.dit.hua.gr/~michail/subpages/libmosp/doxygen.Google Scholar
- Mahdian, M. 2006. Random popular matchings. In Proceedings of the 7th ACM Conference on Electronic Commerce (EC'06). ACM, New York, 238--242. Google ScholarDigital Library
- Manlove, D. F. and Sng, C. T. S. 2006. Popular matchings in the capacitated house allocation problem. In Proceedings of the 14th Annual European Symposium on Algorithms (ESA' 06). Springer-Verlag, Berlin, 492--503. Google ScholarDigital Library
- McCutchen, R. M. 2008. The least-unpopularity-factor and least-unpopularity-margin criteria for matching problems with one-sided preferences. In Proceedings of the 8th Latin American Conference on Theoretical Informatics (LATIN'08). Springer-Verlag, Berlin, 593--604. Google ScholarDigital Library
- Mehlhorn, K. and Naher, S. 1999. LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge, UK. Google ScholarDigital Library
- Mestre, J. 2006. Weighted popular matchings. In Proceedings of Automata, Languages and Programming, 33rd International Colloquium. Springer-Verlag, Berlin, 715--726. Google ScholarDigital Library
- Michail, D. 2007. Reducing rank-maximal to maximum weight matching. Theor. Comput. Sci. 389, 1-2, 125--132. Google ScholarDigital Library
- NBA. 2011 Statistics. www.databasebasketball.com/stats_download.htm.Google Scholar
- Roth, A. E. and Postlewaite, A. 1977. Weak versus strong domination in a market with indivisible goods. J. Math. Econ. 4, 2, 131--137.Google ScholarCross Ref
- Setubal, J. a. C. 1996. Sequential and parallel experimental results with bipartite matching algorithms. Tech. rep. IC-96-09, Institute of Computing, University of Campinas.Google Scholar
- U, L. H., Mamoulis, N., and Mouratidis, K. 2009. A fair assignment algorithm for multiple preference queries. In Proceedings of the VLDB Endowment. http://www.vldb.org/pvldb/2/vldb09-pvldbll.pdf.Google Scholar
- Zhou, L. 1990. On a conjecture by Gale about one-sided matching problems. J. Econ. Theor. 52, 1, 123--135.Google ScholarCross Ref
- Zillow. 2011. www.zillow.com.Google Scholar
Index Terms
- An experimental comparison of single-sided preference matching algorithms
Recommendations
Rank-maximal matchings – structure and algorithms
AbstractLet G = ( A ∪ P , E ) be a bipartite graph where A denotes a set of applicants, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum ...
A note on generalized matching preclusion in bipartite graphs
AbstractFor a graph with an even number of vertices, the matching preclusion number is the minimum number of edges whose deletion results in a graph with no perfect matchings. The conditional matching preclusion number, introduced as an ...
Popular matchings: structure and algorithms
An instance of the popular matching problem (POP-M) consists of a set of applicants and a set of posts. Each applicant has a preference list that strictly ranks a subset of the posts. A matching M of applicants to posts is popular if there is no ...
Reviews
Michael G. Murphy
In this paper, Michail reports on the experimental use of several matching algorithms with single-sided preferences (as opposed to both-sided, which is known as the stable marriage problem). In particular, Michail assesses the quality of matches based on rank-maximal algorithms and on popular matching algorithms compared to the standard minimum weight matching algorithm. Unpopularity of matchings is also considered. The experiments involved structured random data plus extractions from real-world databases. The introductory section presents the problem, including key definitions, a historical overview, and the experimental strategy to be followed. The second section is an introduction to the specific algorithms that are studied as alternatives to the minimum weight matching algorithm, including rank-maximal algorithms (with variations) and popular matchings. A table summarizes the algorithms (with variations) together with running times and space. Rather than being encyclopedic regarding the algorithms, the author provides key summary information and discussion, with references to the original papers for further details. The third section provides insight on how datasets were generated, both structures for random generation and extraction from existing (real estate and National Basketball Association) databases. In the fourth section, the experimental environment and results are discussed and summarized in six tables. The results include running times, unpopularity factors, and various rank characteristics compared to minimum weight matching. In addition to a brief conclusion, there are 29 current and historical references listed. The paper is well organized, insightful, and technically precise. Michail has produced significant experimental results for those with an interest in single-side pattern matching. Online Computing Reviews Service
Access critical reviews of Computing literature here
Become a reviewer for Computing Reviews.
Comments