Fixed-Parameter Tractability of the (1+1) Evolutionary Algorithm on Random Planted Vertex Covers

Abstract

We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every $O(n \log n)$ steps will find a cover at least as small as the planted cover in polynomial time for sufficiently dense random graphs $p > 0.71$. For superlogarithmic planted covers, we prove that the (1+1) EA finds a solution in fixed-parameter tractable time in expectation. We complement these theoretical investigations with a number of computational experiments that highlight the interplay between planted cover size, graph density and runtime.