Deterministic k Routing on Meshes With Applications to Worm Hole Routing

In k routing each of the n processing units of an n n mesh connected computer initially holds packet which must be routed such that any processor is the destination of at most k packets This problem re ects practical desire for routing better than the popular routing of permutations k routing also has implications for hot potato worm hole routing which is of great importance for real world systems We present a near optimal deterministic algorithm run ning in p k n O n steps We give a second algo rithm with slightly worse routing time but working queue size three Applying this algorithm considerably reduces the routing time of hot potato worm hole routing Non trivial extensions are given to the general l k routing problem and for routing on higher dimensional meshes Fi nally we show that k k routing can be performed in O k n steps with working queue size four Hereby the hot potato worm hole routing problem can be solved in O k n