Verifying the concentration property of permutation networks by BDDs

Abstract

A concentrator is a circuit with n inputs and m ≤ n outputs that can route any given subset of k ≤ m valid inputs to k of its m outputs. Concentrator circuits are important for many applications, in particular, for the design of interconnection networks. The design of concentrator circuits is however a challenging task that has already been considered in many research papers. All practical implementations aim at configuring the switches of a permutation network so that it behaves as a concentrator. In this paper, we present methods to analyze various properties of permutation networks by means of binary decision diagrams (BDDs). In particular, we can check whether it is possible to use a considered permutation network as a concentrator or even as a binary sorter. While our method can be applied to all permutation networks, we consider some particular permutation networks and verify that some of them can be used as concentrators and even as binary sorters provided that a specific permutation of the outputs is added.