Structural Decomposition Methods and What They are Good For

Markus Aschinger (1) , Conrad Drescher (1) , Georg Gottlob (1, 2) , Peter Jeavons (1) , Evgenij Thorstensen (1)

1 OUCL - Computing Laboratory
2 Oxford-Man - Oxford-Man Institute of Quantitative Finance

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.

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Markus Aschinger, Conrad Drescher, Georg Gottlob, Peter Jeavons, Evgenij Thorstensen. Structural Decomposition Methods and What They are Good For. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.12-28. ⟨hal-00573592v2⟩