Self-routing superconcentrators

Abstract

We show how to construct, for each n, a system Sn with the following properties. (1) The sys-Tem Sn has n inputs, n outputs, and O(n) components, each of which is of one of a fixed finite number of finite- state machines, and is connected to a fixed finite number of other components through cables, each of which carries signals from a fixed finite alphabet. (2) When some of the inputs, and an equal number of outputs, are "marked" (by the presentation of a certain signal), then after O(logn) steps (a time proportional to the "diameter" of the network) the system will establish a set of disjoint paths from the marked inputs to the marked out-puts. The construction of these "self-routing supercon- centrators" incorporates some methodological improvements in the exploitation of expanders that can also be used to improve results on self-routing non-blocking networks (due to Arora, Leigh ton and Maggs), fault-Tolerant packet-routing networks (due to Leighton and Maggs) and token-distribution algorithms (due to Peleg and Upfal).