ON ARBITRARY SIZE WAKSMAN NETWORKS AND THEIR VULNERABILITY

Abstract

Motivated by problems in telecommunication satellites, we investigate rearrangeable permutation networks made of binary switches. A simple counting argument shows that the number of switches necessary to build a n × n rearrangeable networks (i.e. capable of realizing all one-to-one mappings of its n inputs to its n outputs) is at least ⌈ log 2 (n!) ⌉ = n log 2 n - n log 2 e + o(n) as n → ∞. For n = 2 r , the r-dimensional Beneš network gives a solution using [Formula: see text] switches. Waksman, and independently Goldstein and Leibholz, improved these networks using n log 2 n - n + 1 switches. We provide an extension of this result to arbitrary values of n, using [Formula: see text] switches. Finally the fault-tolerance issue of these networks is discussed.