  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.
