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Acta Informatica

, Volume 15, Issue 4, pp 329–346 | Cite as

Efficient algorithms for finding maximum matchings in convex bipartite graphs and related problems

  • W. LipskiJr.
  • F. P. Preparata
Article

Summary

A bipartite graph G=(A, B, E) is convex on the vertex set A if A can be ordered so that for each element b in the vertex set B the elements of A connected to b form an interval of A; G is doubly convex if it is convex on both A and B. Letting ¦A¦=m and ¦B¦=n, in this paper we describe maximum matching algorithms which run in time O(m + nA(n)) on convex graphs (where A(n) is a very slowly growing function related to a functional inverse of Ackermann's function), and in time O(m+n) on doubly convex graphs. We also show that, given a maximum matching in a convex bipartite graph G, a corresponding maximum set of independent vertices can be found in time O(m+n). Finally, we briefly discuss some generalizations of convex bipartite graphs and some extensions of the previously discussed techniques to instances in scheduling theory.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • W. LipskiJr.
    • 1
  • F. P. Preparata
    • 1
  1. 1.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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