Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree

Approximating Treewidth, Pathwidth, and Minimum Elimination Tree Height

Approximating Treewidth and Pathwidth of some Classes of Perfect Graphs

In this paper we discuss the problem of finding approximations for the treewidth and pathwidth of cotriangulated graphs, convex graphs, permutation graphs and of cocomparability graphs. For a cotriangulated graph, of which the treewidth is at most k, the pathwidth is at most 3k + 4 and we show there exists an O( n2 ) algorithm finding a path-decomposition with width at most 3k + 4. For convex g...

ISSN 0333-3590 Nondeterministic Graph Searching: From Pathwidth to Treewidth

We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this game-theoretic approach and graph decompositions called q-branched tree decompositions, which can be interpreted as a parameterized version of tre...

Treewidth, Pathwidth and Cospan Decompositions

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small widt...

SAT-Encodings for Special Treewidth and Pathwidth

Decomposition width parameters such as treewidth provide a measurement on the complexity of a graph. Finding a decomposition of smallest width is itself NP-hard but lends itself to a SAT-based solution. Previous work on treewidth, branchwidth and clique-width indicates that identifying a suitable characterization of the considered decomposition method is key for a practically feasible SAT-encod...