Approximation algorithms for digraph width parameters

Approximation algorithms for digraph width parameters

Treewidth of an undirected graph measures how close the graph is to being a tree. Several problems that are NP-hard on general graphs are solvable in polynomial time on graphs with bounded treewidth. Motivated by the success of treewidth, several directed analogues of treewidth have been introduced to measure the similarity of a directed graph to a directed acyclic graph (DAG). Directed treewid...

Approximation Algorithms for Minimum-Width Annuli and Shells

On Digraph Width Measures in Parameterized Algorithmics

In contrast to undirected width measures (such as treewidth or clique-width), which have provided many important algorithmic applications, analogous measures for digraphs such as DAGwidth or Kelly-width do not seem so successful. Several recent papers, e.g. those of Kreutzer–Ordyniak, Dankelmann–Gutin–Kim, or Lampis– Kaouri–Mitsou, have given some evidence for this. We support this direction by...

Are There Any Good Digraph Width Measures?

Several different measures for digraph width have appeared in the last few years. However, none of them shares all the “nice” properties of treewidth: First, being algorithmically useful i.e. admitting polynomial-time algorithms for all MSO1-definable problems on digraphs of bounded width. And, second, having nice structural properties i.e. being monotone under taking subdigraphs and some form ...

Algorithms and obstructions for linear-width and related search parameters

The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e1; : : : ; er) in such a way that for every i = 1; : : : ; r 1, there are at most k vertices incident to edges that belong both to fe1; : : : ; eig and to fei+1; : : : ; erg. In this paper, we give a set of 57 graphs and prove that it is the set of the minimal for...