A step-by-step extending parallelism approach for enumeration of combinatorial objects

Abstract

We present a general step-by-step extending approach to parallel execution of enumeration of combinatorial objects (ECO).Themethodology extends a famous enumeration algorithm,OrderlyGeneration,which allows concurrently generating all objects of size n + 1 from all objects of size n. To the best of our knowledge, this is the first time there is an attempt to plug parallel computing into OrderlyGeneration algorithm for ECO problem. The potential impact of this general approach could be applied for many different servants of ECO problem on scientific computing areas in the future. Our work has applied this strategy to enumerate Orthogonal Array (OA) of strength t, a typical kind of combinatorial objects by using a implementation with MPI paradigm. Several initial results in relation to speedup time of the implementation have been analyzed and given significant efficiency of the proposed approach. © Springer-Verlag Berlin Heidelberg 2010.