Deterministic on-line routing on area-universal networks

Two deterministic routing networks, the pruned butterfly and the sorting fat-tree, are presented. Both networks are area universal, i.e. they can simulate with polylogarithmic slowdown, any other routing network fitting in similar area. Previous area-universal networks were either for the offline problem, where the message set to be routed is known in advance and substantial precomputation is permitted, or involved randomization, yielding results that hold only with high probability. The present networks are the first that are simultaneously deterministic and online, and they use two substantially different routing techniques. The performance of the routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity λ, known as the load factor. The pruned butterfly algorithm runs in time O(λ log²N), where N is the number of possible sources and destinations for messages and λ is assumed to be polynomial in N. The sorting fat-free algorithm runs in O(λ log N + log² N) time for a restricted class of message sets, including partial permutations. Other results include a new type of sorting circuit, an area universal circuit, and an area-time lower bound for routers