On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
We place our focus on the gap between treewidth’s success in producing fixed-parameter polynomial algorithms for hard graph problems, and specifically Hamiltonian Circuit and Max Cut, and the failure of its directed variants (directed tree-width , DAG-width  and kelly-width ) to replicate it in the realm of digraphs. We answer the question of why this gap exists by giving two hardness results: we show that Directed Hamiltonian Circuit is W-hard when the parameter is the width of the input graph, for any of these widths, and that Max Di Cut remains NP-hard even when restricted to DAGs, which have the minimum possible width under all these definitions. Our results also apply to directed pathwidth.
KeywordsTreewidth Digraph decompositions Parameterized Complexity
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- 8.Hunter, P., Kreutzer, S.: Digraph measures: Kelly decompositions, games, and orderings. In: Bansal, N., Pruhs, K., Stein, C. (eds.) SODA, pp. 637–644. SIAM, Philadelphia (2007)Google Scholar