On the difficulty of some shortest path problems

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

Volumn 2607, Issue , 2003, Pages 343-354

  Hershberger, John ^a   Suri, Subhash ^b   Bhosle, Amit ^b  

^a MENTOR GRAPHICS CORPORATION   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIRECTED GRAPHS;

CENTRAL PROBLEMS; K SHORTEST PATH; NEAR-LINEAR TIME; NON NEGATIVES; REPLACEMENT PATHS; SHORTEST PATH; SHORTEST PATH PROBLEM; UNDIRECTED GRAPH;

GRAPH THEORY;

EID: 35248898829     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36494-3_31     Document Type: Article

References (27)

1. N. Alon, Z. Galil, and O. Margalit. On the exponent of the all pairs shortest path problem. In 32nd Symposium on Foundations of Computer Science, 569-575, 1991.
2. A. Archer. Private communication, 2001.
3. A. Archer and E. Tardos. Frugal path mechanisms. In Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 991-999, 2002.
4. M. O. Ball, B. L. Golden, and R. V. Vohra. Finding the most vital arcs in a network. Oper. Res. Letters, 8:73-76, 1989.
5. A. Bar-Noy, S. Khuller, and B. Schieber. The complexity of finding most vital arcs and nodes. Technical Report CS-TR-3539, Institute for Advanced Studies, University of Maryland, College Park, MD, 1995.
6. A. Brander and M. Sinclair. A comparative study of K-shortest path algorithms. In Proc. of 11th UK Performance Engineering Workshop, pages 370-379, 1995.
7. D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652-673, 1998.
8. B. Fortz and M. Thorup. Internet traffic engineering by optimizing OSPF weights. In INFOCOM, pages 519-528, 2000.
9. M. Fredman. New bounds on the complexity of the shortest path problem. SIAM J. of Computing, 5:83-89, 1976.
10. E. Hadjiconstantinou and N. Christofides. An efficient implementation of an algorithm for finding K shortest simple paths. Networks, 34(2):88-101, September 1999.
11. J. Hershberger and S. Suri. Vickrey prices and shortest paths: What is an edge worth? In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pages 252-259, 2001.
12. J. Hershberger, M. Maxel, and S. Suri. Finding the k Shortest Simple Paths: A New Algorithm and its Implementation. To appear in Proc. of ALENEX, 2003.
13. D. R. Karger, D. Koller, and S. J. Phillips. Finding the hidden path: Time bounds for all-pairs shortest paths. SIAM J. Comput., 22:1199-1217, 1993.
14. N. Katoh, T. Ibaraki, and H. Mine. An efficient algorithm for k shortest simple paths. Networks, 12:411-427, 1982.
15. D. Kirkpatrick and S. Reisch. Upper bounds for sorting integers on random access machines. Theoretical Computer Science, 28(3):263-276, 1984.
16. E. L. Lawler. A procedure for computing the K best solutions to discrete optimization problems and its application to the shortest path problem. Management Science, pages 401-405, 1972.
17. K. Malik, A. K. Mittal, and S. K. Gupta. The k most vital arcs in the shortest path problem. Oper. Res. Letters, 8:223-227, 1989.
18. E. Martins and M. Pascoal. A new implementation of Yen's ranking loopless paths algorithm. Submited for publication, Universidade de Coimbra, Portugal, 2000.
19. E. Martins, M. Pascoal, and J. Santos. A new algorithm for ranking loopless paths. Technical report, Universidade de Coimbra, Portugal, 1997.
20. E. Nardelli, G. Proietti, and P. Widmayer. Finding the most vital node of a shortest path. In Proc. COCOON, 2001.
21. N. Nisan and A. Ronen. Algorithmic mechanism design. In Proc. 31st Annu. ACM Sympos. Theory Comput., 1999.
22. W. J. Paul and J. Simon. Decision trees and random access machines. In Proc. International Symp. on Logic and Algorithmic, pages 331-340, 1980.
23. A. Perko. Implementation of algorithms for K shortest loopless paths. Networks, 16:149-160, 1986.
24. J. Y. Yen. Finding the K shortest loopless paths in a network. Management Science, 17:712-716, 1971.
25. J. Y. Yen. Another algorithm for finding the K shortest loopless network paths. In Proc. of 41st Mtg. Operations Research Society of America, volume 20, 1972.
26. U. Zwick. All Pairs Shortest Paths in Weighted Directed Graphs-exact and almost exact algorithms. In Proc. IEEE Symposium on Foundations of Computer Science, 310-319, 1998.
27. U. Zwick. All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication. In Electronic Colloquium on Computational Complexity, 2000.