On the algorithmic effectiveness of digraph decompositions and complexity measures

Lampis, M; Kaouri, G; Mitsou, V

dc.contributor.author	Lampis, M	en
dc.contributor.author	Kaouri, G	en
dc.contributor.author	Mitsou, V	en
dc.date.accessioned	2014-03-01T01:36:33Z
dc.date.available	2014-03-01T01:36:33Z
dc.date.issued	2011	en
dc.identifier.issn	1572-5286	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21331
dc.subject	Digraph decompositions	en
dc.subject	Parameterized complexity	en
dc.subject	Treewidth	en
dc.subject.classification	Operations Research & Management Science	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Complexity measures	en
dc.subject.other	Digraph decomposition	en
dc.subject.other	Graph problems	en
dc.subject.other	Hamiltonian circuits	en
dc.subject.other	Hardness result	en
dc.subject.other	Input graphs	en
dc.subject.other	MAX CUT	en
dc.subject.other	NP-hard	en
dc.subject.other	Parameterized	en
dc.subject.other	Parameterized complexity	en
dc.subject.other	Pathwidth	en
dc.subject.other	Polynomial algorithm	en
dc.subject.other	Tree-width	en
dc.subject.other	Algorithms	en
dc.subject.other	Graph theory	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Parameterization	en
dc.subject.other	Parallel processing systems	en
dc.title	On the algorithmic effectiveness of digraph decompositions and complexity measures	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.disopt.2010.03.010	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.disopt.2010.03.010	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	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 [13]), DAG-width (Obdrzalek, 20061141) and Kelly-width (Hunter and Kreutzer, 2007[15]) 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[2]-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[2]-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. (C) 2010 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Discrete Optimization	en
dc.identifier.doi	10.1016/j.disopt.2010.03.010	en
dc.identifier.isi	ISI:000289018300012	en
dc.identifier.volume	8	en
dc.identifier.issue	1	en
dc.identifier.spage	129	en
dc.identifier.epage	138	en