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A Simple Parallel Algorithm for the Single-Source Shortest Path Problem on Planar Digraphs

We present a simple parallel algorithm for the single-source shortest path problem in planar digraphs with nonnegative real edge weights. The algorithm runs on the EREW PRAM model of parallel computation in O((n2e + n1−e) log n) time, performing O(n2+e log n) work for any 0<e<1/2. The strength of the algorithm is its simplicity, making it easy to implement, and presumably quite efficient in practice. The algorithm improves upon the work of all previous algorithms. The work can be further reduced to O(n2+e, by plugging in a less practical, sequential planar shortest path algorithm. Our algorithm is based on a region decomposition of the input graph, and uses a well-known parallel implementation of Dijkstra's algorithm.