A Parallel FPT Application For Clusters

Fixed-parameter tractability (FPT ) techniques have recently been successful in solving NP-complete problem instances of practical importance which were too large to be solved with previous methods. In this paper we show how to enhance this approach through the addition of parallelism, thereby allowing even larger problem instances to be solved in practice. More precisely, we demonstrate the potential of parallelism when applied to the bounded-tree search phase of FPT algorithms. We apply our methodology to the k-VERTEX COVER problem which has important applications, e.g., in multiple sequence alignments for computational biochemistry. We have implemented our parallel FPT method for the k-VERTEX COVER problem using C and the MPI communication library, and tested it on a PC cluster. This is the first experimental examination of parallel FPT techniques. We have tested our parallel k-VERTEX COVER method on protein sequences obtained from the National Center for Biotechnology Information. As part of our experiments, we solved larger instances of k-VERTEX COVER than in any previously reported implementations. For example, our code can solve problem instances with k ≥ 400 in less than 1.5 hours. Since our parallel FPT algorithm requires only very little communication between processors, we expect our method to also perform well on Grids.