A Divide and Conquer Approach to Shortest Paths in Planar Layered Digraphs
نویسندگان
چکیده
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 rst 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(log 3 n) time with n processors in a CREW PRAM. A CRCW version of our algorithm runs in time O(log 2 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.
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