LSV 15th anniversary, February 6–7, 2012, Cachan
Structural decomposition methods, and what they are good for
Talk by
Georg Gottlob
(University of Oxford)
Abstract
This talk 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.
