A Decomposition Algorithm for the All-Pairs Shortest Path Problem on Massively Parallel Computer Architectures

Network optimization on parallel computer architectures has attracted significant interest in recent years. In this paper, we examine the solution of the shortest path problem on massively parallel architectures. We propose a network decomposition strategy that is amenable to parallel implementation and suggest efficient data structures and mappings of the data to the processors that facilitate the solution of the problem. We discuss computational results for the solution of networks of various sizes on the Connection Machine CM-2 (a representative massively parallel architecture) and compare the performance of the algorithm to the performance of serial algorithms implemented on the CRAY X-MP supercomputer and VAXstation 3100. We also present an “idealized” analysis of the algorithm and draw conclusions on properties of decomposition strategies that optimize its performance.