Encyclopedia of Database Systems

Living Edition
| Editors: Ling Liu, M. Tamer Özsu

Spatial Matching Problems

  • Cheng Long
  • Raymond Chi-Wing Wong
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7993-3_80711-1


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 = { p1, p2, p3} and O = { o1, o2, o3}. Then, {(p1, o1), (p2, o2), (p3, o3)} is a matching with three pairs, but {(p1, o1), (p1, o2)} is not a matching since p1 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 the same time: (i)...

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Recommended Reading

  1. 1.
    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.Google Scholar
  2. 2.
    Ahuja RK, Magnanti TL, Orlin JB. Network flows: theory, algorithms, and applications. Englewood Cliffs: Prentice Hall; 1993.zbMATHGoogle Scholar
  3. 3.
    Burkard RE, Dell’Amico M, Martello S. Assignment problems. Philadelphia: Society for Industrial Mathematics; 2009.CrossRefzbMATHGoogle Scholar
  4. 4.
    Efrat A, Itai A, Katz MJ. Geometry helps in bottleneck matching and related problems. Algorithmica. 2001;31(1):1–28.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gabow HN, Tarjan RE. Algorithms for two bottleneck optimization problems. J Algorithms, 1988;9(3):411–17.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gale D, Shapley L. College admissions and the stability of marriage. Am. Math. Mon. 1962;69:9–15.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gross O. The bottleneck assignment problem. Santa Monica: The Rand Corporation; 1959.Google Scholar
  8. 8.
    Hou UL, Yiu ML, Mouratidis K, Mamoulis N. Capacity constrained assignment in spatial databases. In: SIGMOD, Vancouver; 2008.Google Scholar
  9. 9.
    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.Google Scholar
  10. 10.
    Long C, Wong RC-W, Yu PS, Jiang M. On optimal worst-case matching. In: SIGMOD, New York; 2013.Google Scholar
  11. 11.
    Mehlhorn K. Assigning papers to referees. In: Automata, languages and programming, Rhodes; 2009. p. 1–2.Google Scholar
  12. 12.
    Mouratidis K, Mamoulis N. Continuous spatial assignment of moving users. VLDB J. 2010;19(2): 141–60.CrossRefGoogle Scholar
  13. 13.
    Munkres J. Algorithms for the assignment and transportation problems. J Soc Ind Appl Math. 1957;5(1):32–8.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wong RC-W, Tao Y, Fu AW-C, Xiao X. On efficient spatial matching. In VLDB, Vienna; 2007.Google Scholar

Copyright information

© Springer Science+Business Media LLC 2014

Authors and Affiliations

  1. 1.School of Electronics, Electrical Engineering and Computer ScienceQueen’s University BelfastKowloonHong Kong
  2. 2.Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyClear Water Bay, KowloonHong Kong

Section editors and affiliations

  • Dimitris Papadias
    • 1
  1. 1.Dept. of Computer Science and Eng.Hong Kong Univ. of Science and TechnologyKowloonHong Kong SAR