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Encyclopedia of Database Systems pp 1–3Cite as

Spatial Matching Problems

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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...

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Recommended Reading

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Authors and Affiliations

  1. School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Kowloon, Hong Kong

    Cheng Long

  2. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Raymond Chi-Wing Wong

Authors
  1. Cheng Long
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  2. Raymond Chi-Wing Wong
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Corresponding author

Correspondence to Cheng Long .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, Georgia, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, Ontario, Canada

    M. Tamer Özsu

Section Editor information

  1. Dept. of Computer Science and Eng., Hong Kong Univ. of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, Hong Kong SAR

    Dimitris Papadias

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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

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  • DOI: https://doi.org/10.1007/978-1-4899-7993-3_80711-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4899-7993-3

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