A Repeated Mapping Scheme of Task Modules with Minimum Communication Cost in Hypercube Multicomputers
Joo-Man Kim Kim, Cheol-Hoon Lee Lee · ETRI Journal · 1998
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.