Structural Decomposition Methods and What They are Good For
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.
decompositions
12-28
Regular Paper
Markus
Aschinger
Markus Aschinger
Conrad
Drescher
Conrad Drescher
Georg
Gottlob
Georg Gottlob
Peter
Jeavons
Peter Jeavons
Evgenij
Thorstensen
Evgenij Thorstensen
10.4230/LIPIcs.STACS.2011.12
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode