MPI-I-96-1-012

We present a simple parallel algorithm for the {\em single-source shortest path problem} in {\em planar digraphs} with nonnegative real edge weights. The algorithm runs on the EREW PRAM model of parallel computation in $O((n^{2\epsilon} + n^{1-\epsilon})\log n)$ time, performing $O(n^{1+\epsilon}\log n)$ work for any $0<\epsilon<1/2$. The strength of the algorithm is its simplicity, making it easy to implement, and presumably 474 quite efficient in practice. The algorithm improves upon the work of all previous algorithms. The work can be further reduced to $O(n^{1+\epsilon})$, 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.