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Betweenness centrality is a measure based on shortest paths that attempts to quantify the relative importance of nodes in a network. As computation of betweenness centrality becomes increasingly important in areas such as social network analysis, networks of interest are becoming too large to fit in the memory of a single processing unit, making parallel execution a necessity. Parallelization over the vertex set of the standard algorithm, with a final reduction of the centrality for each vertex, is straightforward but requires Ω(|V|2) storage. In this paper we present a new parallelizable algorithm with low spatial complexity that is based on the best known sequential algorithm. Our algorithm requires O(|V| + |E|) storage and enables efficient parallel execution. Our algorithm is especially well suited to distributed memory processing because it can be implemented using coarse-grained parallelism. The presented time bounds for parallel execution of our algorithm on CRCW PRAM and on distributed memory systems both show good asymptotic performance. Experimental results with a distributed memory computer show the practical applicability of our algorithm.