A Repeated Mapping Scheme of Task Modules with Minimum Communication Cost in Hypercube Multicomputers

This paper deals with the problem of one‐to‐one mapping of 2n task modules of a parallel program to an n‐dimensional hypercube multicomputer so as to minimize the total communication cost during the execution of the task. The problem of finding an optimal mapping has been proven to be NP‐complete. First we show that the mapping problem in a hypercube multicomputer can be transformed into the problem of finding a set of maximum cutsets on a given task graph using a graph modification technique. Then we propose a repeated mapping scheme, using an existing graph bipartitioning algorithm, for the effective mapping of task modules onto the processors of a hypercube multicomputer. The repeated mapping scheme is shown to be highly effective on a number of test task graphs; it increasingly outperforms the greedy and recursive mapping algorithms as the number of processors increases. Our repeated mapping scheme is shown to be very effective for regular graphs, such as hypercube‐isomorphic or ‘almost’ isomorphic graphs and meshes; it finds optimal mappings on almost all the regular task graphs considered.