Solving large FPT problems on coarse-grained parallel machines

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 in, for example, the analysis of 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 32-node Beowulf cluster. This is the first experimental examination of parallel FPT techniques. 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 kX400 in less than 1:5 h: r 2003 Elsevier Inc. All rights reserved. ARTICLE IN PRESS Research partially supported by the Natural Sciences and Engineering Research Council of Canada and by the Pacific Institute of Mathematical Sciences (PIMS). Corresponding author. E-mail addresses: [email protected] (J. Cheetham), [email protected] (F. Dehne), [email protected] (A. Rau-Chaplin), [email protected] (U. Stege), [email protected] (P.J. Taillon). URLs: http://www.carleton.ca/~jcheetha, http://www.dehne.net, http://www.cs.dal.ca/~arc, http://www.csr.uvic. ca/~stege. 0022-0000/03/$ see front matter r 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0022-0000(03)00075-8