Tuning block-parallel all-pairs shortest path algorithm for efficient multi-core implementation

Abstract

Finding shortest paths in a weighted graph is one of the key problems in computer-science, which has numerous practical applications in multiple domains. This paper analyzes the parallel blocked all-pairs shortest path algorithm at the aim of evaluating the influence of the multi-core system and its hierarchical cache memory on the parameters of algorithm implementation depending on the size of the graph and the size of distance matrix’s block. It proposes a technique of tuning the block-size to the given multi-core system. The technique involves profiling tools in the tuning process and allows the increase of the parallel algorithm throughput. Computational experiments carried out on a rack server equipped with two intel xeon e5-2620 v4 processors of 8 cores and 16 hardware threads each have convincingly shown for various graph sizes that the behavior and parameters of the hierarchical cache memory operation don’t depend on the graph size and are determined only by the distance matrix’s block size. To tune the algorithm to the target multi-core system, the preferable block size can be found once for the graph size whose in-memory matrix representation is larger than the size of cache shared among all processor’s cores. Then this block-size can be reused on graphs of bigger size for efficient solving the all-pairs shortest path problem.