A Divide-and-Conquer Approach to Shortest Paths in Planar Layered Digraphs (1992)
BibTeX
@MISC{Sairam92adivide-and-conquer,
author = {S. Sairam and Roberto Tamassia and Jeffrey Scott Vitter},
title = {A Divide-and-Conquer Approach to Shortest Paths in Planar Layered Digraphs},
year = {1992}
}
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Abstract
Computing shortest paths in a directed graph has received considerable attention in the sequential RAM model of computation. However, developing a polylog-time parallel algorithm that is close to the sequential optimal in terms of the total work done remains an elusive goal. We present a first step in this direction by showing that for an n-node planar layered digraph with nonnegative edge-weights the shortest path between any two vertices can be computed in O(log³ n) time with n processors in a CREW PRAM. A CRCW version of our algorithm runs in time O(log² n log log n) and uses n log n/log log n processors. Our results make use of the existence of special kinds of separators in planar layered digraphs, called one-way separators, to implement a divide and conquer solution.
