Free-space optical interconnection is used to fashion a reconfigurable network. Since network reconfiguration is expensive compared to message transmission in such networks, latency hiding techniques can be used to increase the performance of collective communications operations. Berthome and Ferreira have recently proposed a broadcasting algorithm for their loosely-coupled optically reconfigurable parallel computer where they have shown that the total number of nodes, N(S), informed up to step S follows a recurrence relation. We have adapted their algorithm to our reconfigurable optical network, RON (K, N), which has slightly different modeling. We present a new analysis of this broadcasting algorithm on our network. This paper contributes by providing closed formulations for the N(S) that yield the termination time for both single-port and k-port modeling. The derived closed formulate are easier to computer than the recurrence relations.
Complexity of Collective Communications on NoCs
