Parallel maximum independent set in convex bipartite graphs

A bipartite graph G = ( V, W, E) is called convex if the vertices in W can be ordered in such a way that the elements of W adjacent to any vertex υ ϵ V form an interval (i.e. a sequence consecutively numbered vertices). Such a graph can be represented in a compact form that requires O( n) space, whe...

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Vydáno v:Information processing letters Ročník 59; číslo 6; s. 289 - 294
Hlavní autoři: Czumaj, Artur, Diks, Krzysztof, Przytycka, Teresa M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 23.09.1996
Elsevier Science
Elsevier Sequoia S.A
Témata:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Bipartite graphs
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Convex graphs
Exact sciences and technology
Graph theory
Graphs
Independent set
Information processing
Information retrieval. Graph
Mathematics
PRAM algorithms
Sciences and techniques of general use
Studies
Theoretical computing
Independent set
Convex graphs
PRAM algorithms
Bipartite graphs
Graph theory
Convex graph
Algorithms
Convexity
Bipartite graph
ISSN:0020-0190, 1872-6119
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Shrnutí:A bipartite graph G = ( V, W, E) is called convex if the vertices in W can be ordered in such a way that the elements of W adjacent to any vertex υ ϵ V form an interval (i.e. a sequence consecutively numbered vertices). Such a graph can be represented in a compact form that requires O( n) space, where n = max{¦V¦, ¦W¦}. Given a convex bipartite graph G in the compact form Dekel and Sahni designed an O( log 2( n))-time, n-processor EREW PRAM algorithm to compute a maximum matching in G. We show that the matching produced by their algorithm can be used to construct optimally in parallel a maximum set of independent vertices. Our algorithm runs in O( logn) time with n logn processors on an Arbitrary CRCW PRAM.
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ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(96)00131-7