Computing transitive closure on systolic arrays of fixed size

Authors:
Björn Lisper
Affiliations:
Swedish Institute of Computer Science, P.O. Box 1263, S-164 28 Kista, Sweden
Venue:
Distributed Computing
Year:
1991

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Abstract

Forming the transitive closure of a binary relation (or directed graph) is an important part of many algorithms. When the relation is represented by a bit matrix, the transitive closure can be efficiently computed in parallel in a systolic array.Here we propose two novel ways of computing the transitive closure of an arbitrarily big graph on a systolic array of fixed size. The first method is a simple partitioning of a well-known systolic algorithm for computing the transitive closure. The second is a block-structured algorithm. This algorithm is suitable for execution on a systolic array that can multiply fixed size bit matrices and compute transitive closure of graphs with a fixed number of nodes. The algorithm is, however, not limited to systolic array implementations; it works on any parallel architecture that can perform these bit matrix operations efficiently.The shortest path problem, for directed graphs with weighted edges, can also be solved in the same manner, devised above, as the transitive closure is computed.