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

Journal of Parallel and Distributed Computing

Volumn 60, Issue 9, 2000, Pages 1103-1124

  Träff, Jesper L ^a   Zaroliagis, Christos D ^b  

^a NEC LABORATORIES EUROPE   (Germany)

^b UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242599131     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.2000.1646     Document Type: Article

References (21)

1. Ahuja R. K., Magnanti T. L., Orlin J. B. Network Flows. 1993;Prentice-Hall, New York.
2. Brodal G. S. Worst-case efficient priority queues. Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA). 1996;. p. 52-58.
3. Brodal G. S., Träff J. L., Zaroliagis C. D. A parallel priority queue with constant time operations. J. Parallel Distrib. Comput. 49:1998;4-21.
4. Cohen E. Efficient parallel shortest-paths in digraphs with a separator decomposition. J. Algorithms. 21:1996;331-357.
5. Discroll J. R., Gabow H. N., Shrairman R., Tarjan R. E. Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation. Comm. Assoc. Comput. Mach. 31:1988;1343-1354.
6. Frederickson G. N. Fast algorithms for shortest paths in planar graphs with applications. SIAM J. Comput. 16:1987;1004-1022.
7. Fredman M. L., Tarjan R. E. Fibonacci heaps and their uses in improved network optimization algorithms. J. Assoc. Comput. Mach. 34:1987;596-615.
8. H. Gazit, and, G. L. Miller, An O( n log(n)) optimal parallel algorithm for a separator for planar graphs, Unpublished manuscript, 1987.
9. Gazit H., Miller G. L. A parallel algorithm for finding a separator in planar graphs. Proceedings of the 28th IEEE Symposium on Foundations of Computer Science (FOCS). 1987;. p. 238-248.
10. Hagerup T. Optimal parallel algorithms on planar graphs. Inform. and Comput. 84:1990;71-96.
11. JáJá J. An Introduction to Parallel Algorithms. 1992;Addison-Wesley, Reading.
12. Keßler C. W., Träff J. L. Language and library support for practical PRAM programming. Parallel Comput. 25:1999;105-135.
13. Klein P. On Gazit and Miller's parallel algorithm for planar separators: Achieving greater efficiency through random sampling. 5th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA). 1993;. p. 43-49.
14. Klein P., Rao S., Rauch M., Subramanian S. Faster shortest-path algorithms for planar graphs. Proceedings of the 26th Symposium on Theory of Computation (STOC). 1994;. p. 27-37.
15. Klein P. N., Reif J. H. An efficient parallel algorithm for planarity. J. Comput. System Sci. 37:1988;190-246.
16. Klein P. N., Subramanian S. A linear-processor, polylog-time algorithm for shortest paths in planar graphs. 34th Symposium on Foundations of Computer Science (FOCS). 1993;. p. 259-270.
17. Lipton R. J., Tarjan R. E. A separator theorem for planar graphs. SIAM J. Appl. Math. 36:1979;177-189.
18. Miller G. L. Finding small simple cycle separators for 2-connected planar graphs. J. Comput. System Sci. 32:1986;265-279.
19. Phillips C. A. Parallel graph contraction. Proceedings of the 1989 ACM Symposium on Parallel Algorithms and Architectures (SPAA). 1989;. p. 148-157.
20. Ramachandran V., Reif J. H. Planarity testing in parallel. J. Comput. System Sci. 49:1994;517-561.
21. Träff J. L., Zaroliagis C. D. A simple parallel algorithm for the single-source shortest path problem on planar digraphs. Parallel Algorithms for Irregularly Structured Problems - IRREGULAR '96. Lecture Notes in Computer Science. 1117:1996;Springer-Verlag, Berlin/New York. p. 183-194.