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Theoretical Computer Science
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Theoretical Computer Science
Article . 2005
License: Elsevier Non-Commercial
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Theoretical Computer Science
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Generating bicliques of a graph in lexicographic order

Authors: Vânia M. Félix Dias; Celina M. H. de Figueiredo; Jayme Luiz Szwarcfiter;

Generating bicliques of a graph in lexicographic order

Abstract

A complete bipartite set \(B\) of a graph is a subset of vertices admitting a bipartition \(B=X\cup Y\) such that both \(X\) and \(Y\) are independent sets and all vertices of \(X\) are adjacent to those of \(Y\). If both \(X,Y\neq \emptyset\), then \(B\) is called proper. A biclique is a maximal proper complete bipartite set of a graph. The authors present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. They show also that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The paper contains an extension of results of \textit{D. S. Johnson, C. H. Papadimitriou} and \textit{M. Yannakakis} [``On generating all maximal independent sets'', Inf. Process. Lett. 27, 119--123 (1988; Zbl 0654.68086)].

Keywords

Lexicographic order, Enumeration, Analysis of algorithms and problem complexity, enumeration, NP-completeness, Theoretical Computer Science, Biclique, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), biclique, Graph theory (including graph drawing) in computer science, Graph algorithms (graph-theoretic aspects), lexicographic order, polynomial-time delay, Polynomial-time delay, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), algorithmics, Algorithms, NP-complete, Computer Science(all)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
27
Top 10%
Top 10%
Average
hybrid