2026-08-19T08:50:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:2996 2024-03-06T10:33:42Z ddc:004 open_access

Structural Decomposition Methods and What They are Good For Aschinger, Markus Drescher, Conrad Gottlob, Georg Jeavons, Peter Thorstensen, Evgenij decompositions This paper reviews structural problem decomposition methods, such as tree and path decompositions. It is argued that these notions can be applied in two distinct ways: Either to show that a problem is efficiently solvable when a width parameter is fixed, or to prove that the unrestricted (or some width-parameter free) version of a problem is tractable by using a width-notion as a mathematical tool for directly solving the problem at hand. Examples are given for both cases. As a new showcase for the latter usage, we report some recent results on the Partner Units Problem, a form of configuration problem arising in an industrial context. We use the notion of a path decomposition to identify and solve a tractable class of instances of this problem with practical relevance. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Aschinger and Conrad Drescher and Georg Gottlob and Peter Jeavons and Evgenij Thorstensen 2011 Is Part Of LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2011.12 urn:nbn:de:0030-drops-29960 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.12 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode