Pareto complexity of two-parameter FPT problems: A case study for partial vertex cover

Abstract

We propose a framework for the complexity of algorithms for FPT problems with two separate parameters k,m and with exponential time bounds O*(xk ym) where x,y > 1 are constant bases. An optimal combination of bases x,y can be chosen depending on the ratio m/k. As a first illustration we apply the framework to the problem of finding, in a graph, a vertex cover of size k that leaves at most m edges uncovered. We report the best branching rules we could find so far, for all ranges of ratio m/k. © 2009 Springer-Verlag.