Exact computation of maximum induced forest

Abstract

We propose a backtrack algorithm that solves a generalized version of the Maximum Induced Forest problem (MIF) in time O*(1.8899 n). The MIF problem is complementary to finding a minimum Feedback Vertex Set (FVS), a well-known intractable problem. Therefore the proposed algorithm can find a minimum FVS as well. To the best of our knowledge, this is the first algorithm that breaks the O*(2 n) barrier for the general case of FVS. Doing the analysis, we apply a more sophisticated measure of the problem size than the number of nodes of the underlying graph. © Springer-Verlag Berlin Heidelberg 2006.