Subexponential parameterized algorithms collapse the W-hierarchy

Abstract

It is shown that for essentially all MAX SNP-hard optimization problems finding exact solutions in subexponential time is not possible unless W[1] = FPT. In particular, we show that O(2o(k)p(n)) parameterized algorithms do not exist for Vertex Cover, Max Cut, Max c-Sat, and a number of problems on bounded degree graphs such as Dominating Set and Independent Set, unless W[1] = FPT. Our results are derived via an approach that uses an extended parameterization of optimization problems and associated techniques to relate the parameterized complexity of problems in FPT to the parameterized complexity of extended versions that are W[1]-hard. © 2011 Springer-Verlag Berlin Heidelberg.