Deterministic On-Line Routing on Area-Universal Networks (Extended Abstract)

We present two deterministic routing networks, the pruned butterfly and the sorting fat-tree. Both networks are area-universal, i.e., they can simulate any other routing network fitting in similar area with polylogarithmic slowdown. Previous area-universal networks were either for the off-line 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. Our two networks are the first that are simultaneously deterministic and on-line, and they use two substantially different routing techniques. The performance of our routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity X known as the load factor. The pruned butterfly algorithm runs in time O(X log' N), where N is the number of possible sources and destinations for messages and X is assumed to be polynomial in N . The sorting fat-tree algorithm runs in O(X log N + log2 N) time for a restricted class of message sets including partial permutations. Other results of this work include a new type of sorting circuit, an area-universal circuit, and an area-time lower bound for routers.