On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
2011 (English)In: Discrete Optimization, ISSN 1572-5286, Vol. 8, no 1, 129-138 p.Article in journal (Refereed) Published
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 treewidth (Johnson et al., 2001 ), DAG-width (Obdrzalek, 20061141) and Kelly-width (Hunter and Kreutzer, 2007) 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. Along the way, we extend our reduction for DIRECTED HAMILTONIAN CIRCUIT to show that the related MINIMUM LEAF OUTBRANCHING problem is also W-hard when naturally parameterized by the number of leaves of the solution, even if the input graph has constant width. All our results also apply to directed pathwidth and cycle rank.
Place, publisher, year, edition, pages
2011. Vol. 8, no 1, 129-138 p.
Treewidth, Digraph decompositions, Parameterized complexity
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-58604DOI: 10.1016/j.disopt.2010.03.010ISI: 000289018300012OAI: oai:DiVA.org:kth-58604DiVA: diva2:473413
QC 201201092012-01-052012-01-052012-01-09Bibliographically approved