Acta Informatica

, Volume 15, Issue 4, pp 329–346

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

Authors

  • W. LipskiJr.
    • Coordinated Science LaboratoryUniversity of Illinois at Urbana-Champaign
  • F. P. Preparata
    • Coordinated Science LaboratoryUniversity of Illinois at Urbana-Champaign
Article

DOI: 10.1007/BF00264533

Cite this article as:
Lipski, W. & Preparata, F.P. Acta Informatica (1981) 15: 329. doi:10.1007/BF00264533

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.

Copyright information

© Springer-Verlag 1981