Parallel Computing I (1984) 287-294 287 North-Holland Performance evaluation of vector implementations of combinatorial algorithms * Celso RIBEIRO Department of Electrical Engineering~ Catholic Unioersity of Rio de Janeiro, Gavea-Caixa Postal 38063, Rio de Janeiro 22452, Brazil Received June 1984 Abstract. We study the performance and the use of vector computers for the solution of combinatorial optimization problems, particularly dynamic programming and shortest path problems. A general model for performance evaluation and vector implementations for the problems described above are studied. These implementations were done on a CRAY-1 vector computer and the computational re:s. ults obtained show (i) the adequacy of the performance evaluation model and (ii) very important gains concerning computing times, showing that vector computers will be of great importance in the field of combinatorial optimization. Keywords. CRAY-1, combinatorial algorithms, vectorization, performance analysis, dynamic programming, shortest path problems. 1. Introduction Several recent papers (e.g. Bossavit [3], Kuch et al. [13], Rodrigue [14], Dixon and Patel [8]) are oriented toward the development and the analysis of parallel algorithms for problems arising in the field of applied mathematics. In most of the eases, computational results have been obtained by vector implementations on the CRAY-1 computer, one of the fastest computers currently available. However, very few results are available concerning combinatorial optimization algorithms, presently a very important field of research. It was already shown that the complexity of the resolution of some problems can be reduced by the use of parallel algorithms running on parallel computers. Among these problems we have the inner product, the product of two matrices and the sort of the elements of a vector. Cook [5] proved that the class of problems that can be solved in parallel polynomial time (polynomial time with a polynomial number of processors) is the same class of problems that can be solved in sequential polynomial time. This result is very important, since it shows that it is unlikely that we could ever solve hard NP-complete problems (see Garey and Johnson [10]) in (parallel) polynomial time, unless we use a nonpolynomial number of processors running in parallel. Anyway, even if we can not reduce their theoretical complexity, it would be very important * This research was supported by CNPq (Brazilian Council for Scientific and Technological Development) and the computer time spent with the use of the CRAY-1 computer was paid by the Department of Applied Mathematics of CNET (French National Center for Telecommunication Studies). The author acknowledges both institutions for their financial and administrative help. 016%8191/84/$3.00 © 1984, Elsevier Science Publishers B.V. (North-Holland)