Computing fair and bottleneck matchings in geometric graphs

Alon Efrat, Matthew J. Katz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Let A and B be two sets of n points in the plane, and let M be a (one-to-one) matching between .4 and B. Let rain(M), max(M), and Σ(M) denote the length of the shortest edge, the length of the longest edge, and the sum of the lengths of the edges of M respectively. The uniform matching problem (also called the balanced assignment problem, or the fair matching problem) is to find M* U, a matching that minimizes max(M) - rain(M). A minimum deviation matching M* D is a matching that (1/n)Σ(M) – min(M). We present algorithms for computing M* U and M* D in roughly O(n10/3) time. These algorithms are more efficient than the previous O(n4)-time algorithms of Martello and Toth [19] and Gupta and Punnen [11], who studied these problems for general bipartite graphs. We also consider the (non-bipartite version of the) bottleneck matching problem in higher dimensions. We extend the planar results of Chang et al. [4] and Su and Chang [22], and show that given a set A of 2n points in d-space, it is possible to compute a bottleneck matching of A in roughly O(n3/2) time, for d ≤ 6, and in subquadratic time, for d > 6.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings
PublisherSpringer Verlag
Pages116-125
Number of pages10
Volume1178
ISBN (Print)3540620486, 9783540620488
StatePublished - 1996
Externally publishedYes
Event7th International Symposium on Algorithms and Computation, ISAAC 1996 - Osaka, Japan
Duration: Dec 16 1996Dec 18 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1178
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Symposium on Algorithms and Computation, ISAAC 1996
CountryJapan
CityOsaka
Period12/16/9612/18/96

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Efrat, A., & Katz, M. J. (1996). Computing fair and bottleneck matchings in geometric graphs. In Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings (Vol. 1178, pp. 116-125). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1178). Springer Verlag.