Parallelization of All-Pairs-Shortest-Path Algorithms in Unweighted Graph

The design of the network topology of a large-scale parallel computer system can be represented as an order/degree problem in graph theory. To solve the order/degree problem, it is necessary to obtain an all-pairs-shortest-path (APSP) of the graph. Thus, this paper evaluates two parallel algorithms that quickly find the APSP in unweighted graphs and compares their performance. The first APSP algorithm is based on the breadth-first search (BFS-APSP) and the second is based on the adjacency matrix (ADJ-APSP). First, we develop serial algorithms and threaded algorithms using OpenMP, and show that ADJ-APSP is up to 32.34 times faster than BFS-APSP. Next, we develop hybrid-parallel algorithms using OpenMP and MPI, and show that BFS-APSP is faster than ADJ-APSP under certain conditions because the maximum number of processes in BFS-APSP is greater than in ADJ-APSP. In addition, we parallelize ADJ-APSP using a single GPU (NVIDIA Tesla V100) and achieve a speed increase of up to 16.53-fold compared to that of a single CPU. Finally, we evaluate the performance of the algorithms using 128 GPUs and achieve a computation time 101.10 times faster than that using a single GPU. Moreover, it is shown that the calculation time of both algorithms can be greatly reduced when the input graphs are symmetric.