Parameterized complexity: Exponential speed-up for planar graph problems

Abstract

A parameterized problem is fixed parameter tractable if it admits a solving algorithm whose running time on input instance (I; k) is f(k) I α, where f is an arbitrary function depending only on k. Typically, f is some exponential function, e.g., f(k) = ck for constant c. We describe general techniques to obtain growth of the form f(k) = ck for a large variety of planar graph problems. The key to this type of algorithm is what we call the \Layerwise Separation Property of a planar graph problem. Problems having this property include planar vertex cover, planar independent set, and planar dominating set. © 2011 Springer-Verlag Berlin Heidelberg.