Approximation Algorithms for Digraph Width Parameters

TL;DR

This paper introduces approximation algorithms for various digraph width parameters, providing bounds for directed treewidth, pathwidth, DAG-width, and Kelly-width, which facilitate efficient solutions for NP-hard problems.

Contribution

It presents the first approximation algorithms with specific bounds for multiple digraph width measures, extending the applicability of graph decomposition techniques.

Findings

O(sqrt{log n})-approximation for directed treewidth

O(log^{3/2} n)-approximation for directed pathwidth, DAG-width, Kelly-width

Algorithms construct decompositions within these approximation factors

Abstract

Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and Kelly-width are some such notions which generalize treewidth, whereas directed pathwidth generalizes pathwidth. Each of these digraph width measures have an associated decomposition structure. In this paper, we present approximation algorithms for all these digraph width parameters. In particular, we give an O(sqrt{logn})-approximation algorithm for directed treewidth, and an O({\log}^{3/2}{n})-approximation algorithm for directed pathwidth, DAG-width and Kelly-width. Our algorithms construct the corresponding decompositions whose widths are within the above mentioned approximation factors.