Efficient parallel algorithms for planar st-graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1350, Issue , 1997, Pages 224-232

  Atallah, Mikhail J ^a   Chen, Danny Z ^b   Daescu, Ovidiu ^b  

^a Purdue University   (United States)

^b University of Notre Dame   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GRAPHIC METHODS; PARALLEL ALGORITHMS;

ALL PAIRS SHORTEST PATHS; DEPTH FIRST SEARCH; SINGLE SOURCE SHORTEST PATHS;

GRAPH THEORY;

EID: 0242514337     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63890-3_25     Document Type: Conference Paper

References (33)

1. A. Aggarwal and J. Park, "Notes on searching in multidimensional monotone arrays," Proc. 29th Annual IEEE Syrup. on Foundations of Computer Science, 1988, pp. 497-512
2. A. Apostolico, M. J. Atallah, L. L. Larmore, and H. S. McFaddin, "Efficient parallel algorithms for string editing and related problems," SIAM J. Comput., 19 (5) (1990), pp. 968-988
3. M. J. Atallah and S. R. Kosaraju, "An efficient parallel algorithm for the row minima of a totally monotone matrix," J. of Algorithms, 13 (3) (1992), pp. 394-413
4. R. P. Brent, "The parallel evaluation of general arithmetic expressions," J. of the ACM, 21 (2) (1974), pp. 201-206
5. E. Cohen, "Efficient parallel shortest-paths in digraphs with a separator decomposition," J. of Algorithms, 21 (2) (1996), pp. 331-357
6. T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, McGraw-Hill, 1990
7. G. Di Battista and E. Nardelli, "An algorithm for testing planarity of hierarchical graphs," Proc. of International Workshop on Graph-Theoretic Concepts in Computer Science, 1986, Bernierd, pp. 277-289
8. H. Gazit and G. Miller, "A parallel algorithm for finding a separator in planar graphs," Proc. 28th Annual IEEE Symp. on Foundations of Computer Science, 1987, pp. 238-248
9. T. Hagerup, "Planar depth-first search in O(log n) parallel time," SIAM J. Cornput., 19 (1990), pp. 678-704
10. Y. Han, V. Y. Pan, and J. H. Reif, "Efficient parallel algorithms for computing all pair shortest paths in directed graphs," Algorithmica, 17 (4) (1997), pp. 399-415
11. X. He, "Efficient parallel algorithms for series parallel graphs," J. of Algorithms, 12 (1991), pp. 409-430
12. X. He and Y. Yesha, "A nearly optimal parallel algorithm for constructing depth first spanning trees in planar graphs," SIAM J. Comput., 17 (1988), pp. 486-491
13. J. JáJá, An Introduction to Parallel Algorithms, Addison-Wesley, Reading, Massachusetts, 1992
14. J. JáJá and S. Kosaraju, "Parallel algorithms for planar graphs and related problems," IEEE Trans. on Circuits and Systems, 35 (1988), pp. 304-311
15. M. Y. Kao, "All graphs have cycle separators and planar directed depth-first search is in DNC," Lecture Notes in Computer Science, Vol. 319, VLSI Algorithms and Architectures, Proc. of 3rd Aegean Workshop on Computing, Springer-Verlag, New York, 1988, pp. 53-63
16. M. Y. Kao, "Planar strong connectivity helps in parallel depth-first search," SIAM J. Comput., 24 (1995), pp. 46-62
17. M. Y. Kao and P. N. Klein, "Towards overcoming the transitive-closure bottleneck: Efficient parallel algorithms for planar digraphs," J. Computer and System Sciences, 47 (1993), pp. 459-500
18. M. Y. Kao, S.-H. Teng, and K. Toyama, "An optimal parallel algorithm for planar cycle separator," Algorithmica, 14 (1995), pp. 398-408
19. P. N. Klein, "Efficient parallel algorithms for chordal graphs," Proc. 29th Annual IEEE Symp. on Foundations of Computer Science, 1988, pp. 150-161
20. P. N. Klein and S. Subramanian, "A linear-processor polylog-time algorithm for shortest paths in planar graphs," Proc. the 3~th Annual Syrup. on Foundations of Computer Science, 1993, pp. 259-270
21. R. J. Lipton and R. E. Tarjan, "A separator theorem for planar graphs," SIAM J. Algebraic and Discrete Methods, 36 (2), 1979, pp. 177-189
22. R.J. Lipton and R. E. Tarjan, "Applications of a planar separator theorem," SIAM J. Comput., 9 (3) (1980), pp. 615-627
23. G. Miller, "Finding small simple cycle separators for 2-connected planar graphs," J. Computer and System Sciences, 32 (1986), pp. 265-279
24. V. Pan and J. H. Reif, "Fast and efficient solution of path algebra problems," J. Computer and System Sciences, 38 (1989), pp. 494-510
25. V. Pan and J. H. Reif, "The parallel computation of minimum cost paths in graphs by stream contraction," Information Processing Letters, 40 (1991), pp. 79-83
26. J. H. Reif, "Depth-first search is inherently sequential," Information Processing Letters, 20 (1985), pp. 229-234
27. S. Sairam, R. Tamassia, and J. S. Vitter, "An efficient parallel algorithm for shortest paths in planar layered digraphs," Algorithmica, 14 (1995), pp. 322-339
28. G. E. Shannon, "A linear-processor algorithm for depth-first search in planar graphs," Information Processing Letters, 29 (1988), pp. 119-123
29. J. R. Smith, "Parallel algorithms for depth-first search I. Planar graphs," SIAM J. Comput., 15 (1986), pp. 814-830
30. R. Tamassia and F. P. Preparata, "Dynamic maintenance of planar digraphs, with applications," Algorithmica, 5 (1990), pp. 509-527
31. R. Tamassia and J. S. Vitter, "Parallel transitive closure and point location in planar structures," SIAM J. Comput., 20 (4) (1991), pp. 708-725
32. J. Valdes, R. E. Tarjan, and E. L. Lawler, "The recognition of series parallel digraphs," SIAM J. Comput., 11 (1982), pp. 298-313
33. S. Whitesides, "Forms of hierarchy: A selected bibliography," General Systems, 14 (1969), pp. 3-15.