On randomized and deterministic schemes for routing and sorting on fixed-connection networks

Abstract

We give a high-level description of some fundamental randomized and deterministic techniques for routing and sorting on fixedconnection networks such as meshes, hypercubes or point-to-point networks. On the randomized side, we focus on the techniques of randomized routing and random sampling and their use in many algorithms, while our presentation of deterministic algorithms uses the example of the Columnsort algorithm to highlight techniques such as local sorting and deterministic sampling. We then demonstrate that there is a close relationship between the randomized and deterministic techniques presented, and illustrate how this relationship can be used to transform randomized into deterministic algorithms and vice versa. Our main objective here is to provide a more unified perspective on many of the algorithms in the literature, and we do not attempt to provide a complete survey of routing and sorting problems on parallel machines.