Deterministic Routing of h-relations on the Multibutterfly

In this paper we devise an optimal deterministic algorithm for routing h-relations on-line on an N-input/output multibutterfly. The algorithm, which is obtained by generalizing the circuit-switching techniques of [AroraLM96], routes any h-relation with messages of X bits, in O(h(X+log N) steps in the bit model, and in O(h X/\log N+log N) communication steps in the word model. Unlike other recently developed algorithms, our algorithm does not need extra levels of expanders, hence minimizes the layout area. Moreover, the network topology does not depend on h.