Dias, V. M.; de Figueiredo, C. M. & Szwarcfiter, J. L.
(2005):
Generating bicliques of a graph in lexicographic order.
In: Theoretical Computer Science,
Ausgabe/Number: 1-3,
Vol. 337,
Erscheinungsjahr/Year: 2005.
Seiten/Pages: 240 - 248.
[Volltext] [Kurzfassung] [BibTeX]
[Endnote]
An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B=X[union or logical sum]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[not equal to][empty set], then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques.
@article{Dias2005240,
author = {Dias, Vânia M.F. and de Figueiredo, Celina M.H. and Szwarcfiter, Jayme L.},
title = {Generating bicliques of a graph in lexicographic order},
journal = {Theoretical Computer Science},
year = {2005},
volume = {337},
number = {1-3},
pages = {240 - 248},
url = {http://www.sciencedirect.com/science/article/B6V1G-4FD0HTT-3/2/7efa1ee4d7b4823c7315a58b94f2f280},
doi = {DOI: 10.1016/j.tcs.2005.01.014},
issn = {0304-3975},
keywords = {graph, conp, theory, set, independent},
abstract = {An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B=X[union or logical sum]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[not equal to][empty set], then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques.}
}
%0 = article
%A = Dias, Vânia M.F. and de Figueiredo, Celina M.H. and Szwarcfiter, Jayme L.
%D = 2005
%T = Generating bicliques of a graph in lexicographic order
%U = http://www.sciencedirect.com/science/article/B6V1G-4FD0HTT-3/2/7efa1ee4d7b4823c7315a58b94f2f280