Unified all-pairs shortest path algorithms in the chordal hierarchy

Discrete Applied Mathematics

Volumn 77, Issue 1, 1997, Pages 59-71

  Han, K ^a   Sekharan, Chandra N ^b   Sridhar, R ^a  

^a University of Oklahoma   (United States)

^b LOYOLA UNIVERSITY CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040096100     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(96)00103-5     Document Type: Article

References (25)

1. N. Alon, Z. Galil and O. Margalit, On the exponent of the all pairs shortest path problem, Proceedings of the 32nd Foundations of Computer Science (1991) 569-575.
2. M.J. Atallah, D.Z. Chen and D.T. Lee, An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications, Proceedings of the European Symposium on Algorithms, Lecture Notes in Computer Science, Vol. 726 (Springer, Berlin, 1993) 13-24.
3. A. Brandstadt, V. Chepoi and F. Dragan, The algorithmic use of hypertree structure and maximum neighborhood orderings, in: E. Mayr, ed., Proceedings of the Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 903 (Springer, Berlin, 1994) 65-80.
4. D.Z. Chen and D.T. Lee, Solving the all-pair shortest path problem on interval and circular arc graphs, Technical Report #93-3, Department of Computer Science, University of Notre Dame, Indiana, May (1993).
5. B. Cherkassky, A.V. Goldberg and T. Radzik, Shortest path algorithms: theory and experimental evaluation, Technical Report, Stanford University (1993).
6. D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progression, Proceedings of the 19th ACM Symposium on Theory of Computing (1987) 1-6.
7. E. Dahlhaus, Optimal (parallel) algorithms for the all-to-all vertex distances problem for certain graph classes, Proceedings of the Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 657 (Springer, Berlin, 1992) 60-69.
8. M. Golumbic, Algorithmic Theory of Perfect Graphs (Academic Press, New York, 1980).
9. J. Ja'Ja, An Introduction to Parallel Algorithms (Addison-Wesley, Reading, MA, 1992).
10. P. Klein, Parallel algorithms for chordal graphs, in: J.H. Reif, ed., Synthesis of Parallel Algorithms (Morgan Kaufmann, Los Altos, CA, 1993) 341-408.
11. S. Kumar and C.E. Veni Madhavan, A new class of separators and planarity of chordal graphs, Proceedings of the 9th FST & TCS Conference, Lecture Notes in Computer Science, Vol. 405 (Springer, Berlin, 1989) 30-43.
12. A. Lubiw, Doubly lexical orderings of matrices, SIAM J. Comput. 16 (1987) 854-879.
13. T. Ma and J.P. Spinrad, Avoiding matrix multiplication, Proceedings of the Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 484 (Springer, Berlin, 1990) 61-71.
14. A. Proskurowski, Recursive graphs, recursive labelings and shortest paths, SIAM J. Computing 10 (1981) 391-397.
15. V. Radhakrishnan, H.B. Hunt III and R.E. Stearns, On solving systems of linear equations and path problems for bounded-treewidth graphs, Proceedings of the 9th Annual Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 577 (Springer, Berlin, 1992) 109-119.
16. R. Ravi, M.V. Marathe and C. Pandu Rangan, An optimal algorithm to solve the all-pair shortest path problem on interval graphs, Networks 22 (1992) 21-35.
17. F. Romani, Shortest-path problem is not harder than matrix multiplication, IPL 11 (1980) 131-136.
18. B. Schieber and U. Vishkin, On finding lowest common ancestors: simplification and parallelization, SIAM J. Computing 17 (1988) 1253-1262.
19. R. Seidel, On the all-pair-shortest-path problem, Proceedings of the 24th ACM Symposium on Theory of Computing (1992) 745-749.
20. J.P. Spinrad, Doubly lexically ordering of dense 0-1 matrices, Inform. Processing Lett. 45 (1993) 229-235.
21. J.P. Spinrad, private communication.
22. R. Sridhar, D. Joshi and N. Chandrasekharan, Efficient algorithms for shortest distance queries on interval, directed path and circular-arc graphs, Proceedings of the 5th International Conference on Computing and Information (1993) 31-35.
23. R. Sridhar and N. Chandrasekharan, Highly parallelizable problems on sorted intervals, Parallel Comput. 21 (1995) 433-446.
24. R. Sridhar, K. Han and N. Chandrasekharan. Efficient algorithms for shortest distance queries on special classes of polygons, Theoret. Comput. Sci. 140 (1995) 291-300.
25. 2.81 infinite-precision multiplication, IPL 4 (1976) 155-156.