RODRIGUES, Carlos Diego. Limites inferiores para o problema de coloração de vértices via geração de cortes e colunas. 2008. 79 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2005. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-06-08T19:45:39Z No. of bitstreams: 1 2008_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-06-08T19:45:58Z (GMT) No. of bitstreams: 1 2008_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) / Made available in DSpace on 2016-06-08T19:45:58Z (GMT). No. of bitstreams: 1 2008_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) Previous issue date: 2008 / In this work the vertex coloring problem is approached via integer programming. A tighter version of the independent set formulation is used, where the vertex-related constraints are substituted by subgraph-related constraints. Each constraint establishes a lower bound on the number of independent sets intersecting a subgraph H. It is shown a sufficient condition for this inequality to define a facet of the associated polytope. Basically, H is required to be color critical, not included in another color critical subgraph, and to have a connected complement. Also, the column generation algorithm proposed by Mehotra and Trick (INFORMS Journal in Computing, 1996) is adapted to allow the addition of cutting planes and to provide lower bounds along the process, which may abbreviate its end. Some computational experiments are reported. / Neste trabalho abordamos o problema de coloração de vértices via programação inteira. Uma versão expandida da formulação por conjuntos independentes é utilizada para abrigar outras sub-estruturas do grafos além dos vértices. Cada uma dessas sub-estruturas define uma restrição que determina quantos conjuntos independentes são necessarios para cobrir aquele subgrafo. Experimentos com um método de geração de cortes e colunas para o problema são feitos para determinar um limite inferior para um conjunto de instâncias classicas para esse problema a biblioteca DIMACS.

RODRIGUES, Carlos Diego. Limites inferiores para o problema de coloração de vértices via geração de cortes e colunas. 2008. 79 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2008. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-11T11:50:40Z No. of bitstreams: 1 2005_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-14T15:28:23Z (GMT) No. of bitstreams: 1 2005_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) / Made available in DSpace on 2016-07-14T15:28:23Z (GMT). No. of bitstreams: 1 2005_dis_cdrodrigues.pdf: 545679 bytes, checksum: 7cceeca6a76bce10cbde4bfb4ef0ee02 (MD5) Previous issue date: 2008 / In this work the vertex coloring problem is approached via integer programming. A tighter version of the independent set formulation is used, where the vertex-related constraints are substituted by subgraph-related constraints. Each constraint establishes a lower bound on the number of independent sets intersecting a subgraph H. It is shown a sufficient condition for this inequality to define a facet of the associated polytope. Basically, H is required to be color critical, not included in another color critical subgraph, and to have a connected complement. Also, the column generation algorithm proposed by Mehotra and Trick (INFORMS Journal in Computing, 1996) is adapted to allow the addition of cutting planes and to provide lower bounds along the process, which may abbreviate its end. Some computational experiments are reported. / Neste trabalho abordamos o problema de coloração de vértices via programação inteira. Uma versão expandida da formulação por conjuntos independentes é utilizada para abrigar outras sub-estruturas do grafos além dos vértices. Cada uma dessas sub-estruturas define uma restrição que determina quantos conjuntos independentes são necessarios para cobrir aquele subgrafo. Experimentos com um método de geração de cortes e colunas para o problema são feitos para determinar um limite inferior para um conjunto de instâncias classicas para esse problema a biblioteca DIMACS.