R-Kleene: A High-Performance Divide-and-Conquer Algorithm for the All-Pair Shortest Path for Densely Connected Networks

Authors:
Paolo D'Alberto;Alexandru Nicolau
Affiliations:
Department of Electric and Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA;Department of Electric and Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Venue:
Algorithmica
Year:
2007

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Abstract

We propose a novel divide-and-conquer algorithm for the solution of the all-pair shortest-path problem for directed and dense graphs with no negative cycles. We propose R-Kleene, a compact and in-place recursive algorithm inspired by Kleene's algorithm. R-Kleene delivers a better performance than previous algorithms for randomly generated graphs represented by highly dense adjacency matrices, in which the matrix components can have any integer value. We show that R-Kleene, unchanged and without any machine tuning, yields consistently between 1/7 and 1/2 of the peak performance running on five very different uniprocessor systems.