Deterministic 1-k routing on meshes: With applications to worm-hole routing

Abstract

In 1-k routing each of the n2 processing units of an n × n mesh connected computer initially holds 1 packet which must be routed such that any processor is the destination of at most k packets. This problem has great practical importance in itself and by its implications for hot-potato worm-hole routing. We present a near-optimal deterministic algorithm running in (Formula Presented) steps, and an algorithm with slightly worse routing time but working queue size three. Non-trivial extensions are given to l-k routing, and for routing on higher dimensional meshes. We show that under a natural condition 1-k routing can be performed in O(k · n) steps. Finally we show that k-k routing can be performed in O(k⋅·⋅n) steps with working queue size four. Hereby hot-potato worm-hole routing can be performed in O(k3/2· ⋅n) steps.