Definition
A matching is a mapping from the elements of one set to the elements of another set such that each element in one set is mapped to at most one element in another set. For example, assume two sets of objects P = { p 1, p 2, p 3} and O = { o 1, o 2, o 3}. Then, {(p 1, o 1), (p 2, o 2), (p 3, o 3)} is a matching with three pairs, but {(p 1, o 1), (p 1, o 2)} is not a matching since p 1 is involved in two pairs. In general, the number of possible matchings is exponential to the cardinality of P and O; e.g., if | P | = | O | = n, there are n! matchings with n pairs. Usually, among all possible matchings, the aim is to find one that optimizes/satisfies a certain criterion.
Let c(p, o) be the cost of matching p ∈ P with o ∈ O. Optimal matching [13] minimizes the sum of the costs of all pairs. Bottleneck matching [7] minimizes the maximum cost of any pair. Fair matching, also known as the stable marriage problem, returns a matching in which the following conditions cannot hold at...
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Recommended Reading
Abraham D, Cechlarova K, Manlove D, Mehlhorn K. Pareto optimality in house allocation problems. In: 15th international symposium on algorithms and computation, Hong Kong. Lecture notes in computer science, vol 3341; 2004. p. 3–15.
Ahuja RK, Magnanti TL, Orlin JB. Network flows: theory, algorithms, and applications. Englewood Cliffs: Prentice Hall; 1993.
Burkard RE, Dell’Amico M, Martello S. Assignment problems. Philadelphia: Society for Industrial Mathematics; 2009.
Efrat A, Itai A, Katz MJ. Geometry helps in bottleneck matching and related problems. Algorithmica. 2001;31(1):1–28.
Gabow HN, Tarjan RE. Algorithms for two bottleneck optimization problems. J Algorithms, 1988;9(3):411–17.
Gale D, Shapley L. College admissions and the stability of marriage. Am. Math. Mon. 1962;69:9–15.
Gross O. The bottleneck assignment problem. Santa Monica: The Rand Corporation; 1959.
Hou UL, Yiu ML, Mouratidis K, Mamoulis N. Capacity constrained assignment in spatial databases. In: SIGMOD, Vancouver; 2008.
Irving RW, Kavitha T, Mehlhorn K, Michail D, Paluch K. Rank-maximal matchings. In: Proceedings of the fifteenth annual ACM-SIAM symposium on discrete algorithms. Philadelphia: Society for Industrial and Applied Mathematics; 2004. p. 68–75.
Long C, Wong RC-W, Yu PS, Jiang M. On optimal worst-case matching. In: SIGMOD, New York; 2013.
Mehlhorn K. Assigning papers to referees. In: Automata, languages and programming, Rhodes; 2009. p. 1–2.
Mouratidis K, Mamoulis N. Continuous spatial assignment of moving users. VLDB J. 2010;19(2): 141–60.
Munkres J. Algorithms for the assignment and transportation problems. J Soc Ind Appl Math. 1957;5(1):32–8.
Wong RC-W, Tao Y, Fu AW-C, Xiao X. On efficient spatial matching. In VLDB, Vienna; 2007.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media LLC
About this entry
Cite this entry
Long, C., Wong, R.CW. (2014). Spatial Matching Problems. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_80711-1
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7993-3_80711-1
Received:
Accepted:
Published:
Publisher Name: Springer, New York, NY
Online ISBN: 978-1-4899-7993-3
eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering