BibTeX
@MISC{Vatshelle12newwidth,
author = {Martin Vatshelle},
title = {New Width Parameters of Graphs},
year = {2012}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
The main focus of this thesis is on using the divide and conquer technique to efficiently solve graph problems that are in general intractable. We work in the field of parameterized algorithms, using width parameters of graphs that indicate the complexity inherent in the structure of the input graph. We use the notion of branch decompositions of a set function introduced by Robert-son and Seymour to define three new graph parameters, boolean-width, max-imum matching-width (MM-width) and maximum induced matching-width (MIM-width). We compare these new graph width parameters to existing graph parameters by defining partial orders of width parameters. We focus on tree-width, branch-width, clique-width, module-width and rank-width, and include a Hasse diagram of these orders containing 32 graph parameters. We use the size of a maximum matching in a bipartite graph as a set function to define MM-width and show that MM-width never differs by more than a multiplicative factor 3 from tree-width. The main reason for introduc-
Keyphrases
new width parameter set function graph parameter width parameter new graph width parameter maximum induced matching-width new graph parameter main focus main reason maximum matching branch decomposition conquer technique partial order graph problem hasse diagram bipartite graph input graph complexity inherent multiplicative factor parameterized algorithm
