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.
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D'Alberto, P., Nicolau, A. R-Kleene: A High-Performance Divide-and-Conquer Algorithm for the All-Pair Shortest Path for Densely Connected Networks. Algorithmica 47, 203–213 (2007). https://doi.org/10.1007/s00453-006-1224-z
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DOI: https://doi.org/10.1007/s00453-006-1224-z