Pareto Complexity of Two-Parameter FPT Problems: A Case Study for Partial Vertex Cover

We propose a framework for the complexity of algorithms for FPT problems with two separate parameters k, in and with exponential time bounds 0*(x(k)y(m)) where x, y > 1 are constant bases. An optimal combination of bases x,p 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 In edges uncovered. We report the best branching rules we could find so far, for all ranges of ratio m/k.