Randomized smoothing networks

Abstract

A smoothing network is a distributed data structure that accepts tokens on input wires and routes them to output wires. It ensures that however imbalanced the traffic on input wires, the numbers of tokens emitted on output wires are approximately balanced. We study randomized smoothing networks, whose initial states are chosen at random. Randomized smoothing networks require no global initialization, and also require no global reconfiguration after faults. We show that the randomized version of the well-known block smoothing network is 2.36 log ( w ) -smooth with high probability, where w is the number of input or output wires. As a direct consequence, we prove that the randomized bitonic and periodic networks are also O ( log ( w ) ) -smooth with high probability. In contrast, it is known that these networks are ( log w ) -smooth in the worst case.