Abstract
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((n 2ε + n 1−ε) log n) time, performing O(n 2+ε log n) work for any 0<ε<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(n 2+ε, 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.
This work was partially supported by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT), and by the DFG project SFB 124-D6 (VLSI Entwurfsmethoden und Parallelität).
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J.L. Träff and C.D. Zaroliagis, A simple parallel algorithm for the single-source shortest path problem on planar digraphs, Tech. Rep. MPI-I-96-1-012, Max-Planck-Institut für Informatik, Saarbrcken, June 1996.
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© 1996 Springer-Verlag Berlin Heidelberg
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Träff, J.L., Zaroliagis, C.D. (1996). A simple parallel algorithm for the single-source shortest path problem on planar digraphs. In: Ferreira, A., Rolim, J., Saad, Y., Yang, T. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1996. Lecture Notes in Computer Science, vol 1117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030108
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DOI: https://doi.org/10.1007/BFb0030108
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