MM-Width: Observations, Algorithms and Approximations

Abstract

In this thesis we investigate maximum matching-width (MM-width) further. MM-width is a graph width parameter similar to treewidth, related to the number of maximum matchings made in an induced bipartite graph made from partitions over the vertices of a graph. We improve the link between the value of maximum matching-width and the value of treewidth of a graph G to mmw(G) <= tw(G). We also give a bounded dynamic programming algorithm BMMDP to calculate the MM-width of a graph exactly. In addition to the exact algorithm we look into approximating the MM-width of graphs from above by using optimization algorithms based on local search and evolutionary algorithms. In the thesis we also make general observations about maximum matching-width, investigate the MM-width of standard graphs and come up with a set of safe kernelization rules to improve the performance of our algorithms. We also use the link between maximum matching-width and the other width parameters, the MM-widths of standard graphs and widths found during run time to add upper and lower bounds to the exact algorithm.