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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-26112012-161435
Document
Author
Full name
Alexandre da Silva Freire
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Ferreira, Carlos Eduardo (President)
Lucena Filho, Abílio Pereira de
Maculan Filho, Nelson
Wakabayashi, Yoshiko
Xavier, Eduardo Cândido
Title in Portuguese
Empacotamento de bicliques em grafos bipartidos
Keywords in Portuguese
biclique máximo
empacotamento de bicliques
geração de colunas
programação inteira
Abstract in Portuguese
Nesta tese, estudamos o problema de Empacotamento de Bicliques. Um biclique é um grafo bipartido completo. No problema de Empacotamento de Bicliques são dados um inteiro k e um grafo bipartido G e deseja-se encontrar um conjunto de k bicliques, subgrafos de G, dois a dois disjuntos nos vértices, tal que a quantidade total de arestas dos bicliques escolhidos seja máxima. No caso em que k=1, temos o problema de Biclique máximo. Esses dois problemas possuem aplicações na área de Bioinformática. Mantemos neste trabalho um enfoque prático, no sentido de que nosso interesse é resolver instâncias desses dois problemas com tamanho razoavelmente grande. Para isso, utilizamos técnicas de Programação Linear Inteira. Para avaliar os métodos propostos aqui, mostramos resultados de experimentos computacionais feitos com instâncias vindas de aplicações e também com instâncias geradas aleatoriamente.
Title in English
Biclique packing in bipartite graphs
Keywords in English
biclique packing
column generation
integer programming
maximum biclique
Abstract in English
In this thesis, we study the Biclique Packing problem. A biclique is a complete bipartite graph. In the Biclique Packing problem we are given an integer k and a bipartite graph G and we want to find a set of k vertex disjoint bicliques of G, such that the total number of biclique's edges is maximum. When k=1, we have the Maximum Biclique problem. These two problems have applications in Bioinformatics. In this work we keep a practical focus, in the sense that we are interested in solving large size instances of these problems. To tackle these problems, we use Integer Linear Programming techniques. In order to evaluate the methods proposed here, we show results of computational experiments carried out with practical application's instances and also with randomly generated ones.
 
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tese.pdf (884.59 Kbytes)
Publishing Date
2013-01-02
 
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