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Structural Decomposition Methods‚ and What They are Good For

Markus Aschinger‚ Conrad Drescher‚ Georg Gottlob‚ Peter Jeavons and Evgenij Thorstensen


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.

Dortmund‚ Germany
Book Title
Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Invited Paper at STACS 2011