Optimal Processor Mapping for Linear-Constant Communication on k-ary n-cubes

Abstract

In this paper, we address the problem of minimizing link contention of linear-constant communication on wormhole-routed k-ary n-cubes. Our research reveals that, for dimension ordered routing algorithms, the degree of link contention of a linear-constant communication can be quite large. To solve this problem, we propose a new approach called processor mapping. In our approach, processors are remapped according to the given communication(s) so that the new communication(s) can be efficiently realized on the k-ary n-cube network. It is proved that for any set of m linear-constant communications, m≦k-1, these exists a processor mapping such that the new communications have minimum link contention. Several computer simulations are conducted and the results clearly show the advantage of the proposed approach.