Parallel transitive closure computation in highly scalable multiprocessors

Abstract

Computation of transitive closure is a fundamental problem in the area of computer algorithms and among others a central issue in the process of integrating database and knowledgebase systems. Although a plethora of sequential transitive closure algorithms have been developed, parallel transitive closure algorithms are rather scarce. Moreover, the few existing parallel algorithms have severe limitations in terms of (a) load balancing, (b) sufficient utilization of the allocated processors, and (c) in ability to take advantage of highly scalable parallel architectures. In this paper we present and analyze two parallel algorithms — PAR-TC and GPAR-TC — for the computation of the transitive closure of a binary database relation. Algorithm PAR-TC is a straightforward parallelization of an existing sequential algorithm [10,22,14]. In many cases, PAR-TC attains significant speedup over its sequential counterpart. In the worst case the speedup is marginal as this algorithm is also subject to the three limitations stated above. Nevertheless, algorithm GPAR-TC which is is a refinement of PAR-TC remedies all three limitations. In the worst case, GPAR-TC is at least as good as PAR-TC; and if a perfect hashing function is available for each value set of the two attributes of the input binary relation, then the speedup of GPAR-TC over the sequential algorithm is proportional to the number of processors available in the system. This last property makes algorithm GPAR-TC especially suitable for highly scalable parallel architectures.KeywordsParallel AlgorithmCommunication CostTransitive ClosureSequential AlgorithmBoolean MatriceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.