, Volume 15, Issue 4, pp 329346
First online:
Efficient algorithms for finding maximum matchings in convex bipartite graphs and related problems
 W. LipskiJr.Affiliated withCoordinated Science Laboratory, University of Illinois at UrbanaChampaign
 , F. P. PreparataAffiliated withCoordinated Science Laboratory, University of Illinois at UrbanaChampaign
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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.
 Title
 Efficient algorithms for finding maximum matchings in convex bipartite graphs and related problems
 Journal

Acta Informatica
Volume 15, Issue 4 , pp 329346
 Cover Date
 198108
 DOI
 10.1007/BF00264533
 Print ISSN
 00015903
 Online ISSN
 14320525
 Publisher
 SpringerVerlag
 Additional Links
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 Industry Sectors
 Authors

 W. Lipski Jr. ^{(1)}
 F. P. Preparata ^{(1)}
 Author Affiliations

 1. Coordinated Science Laboratory, University of Illinois at UrbanaChampaign, 61801, Urbana, Illinois, USA