Efficient Implementation of the Italiano Algorithms for Updating the Transitive Closure on Associative Parallel Processors

Abstract

We propose a simple data structure for an efficient implementation of the Italiano algorithms for the dynamic updating of the transitive closure of a directed graph represented as adjacency matrix on a model of associative (or content addressable) parallel processors with vertical processing (the STAR–machine). Associative versions of the Italiano algorithms are represented as procedures DeleteArc1 and InsertArc1. We prove the correctness of these procedures and evaluate their time and space complexity. We also present the main advantages of associative versions of the Italiano algorithms.