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An O(n3 (loglogn/logn)5/4) Time Algorithm for All Pairs Shortest Paths

  • Yijie Han
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)

Abstract

We present an O(n 3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths. This algorithm improves on the best previous result of O(n 3/logn) time.

Keywords

Short Path Table Lookup Small Matrice Medium Matrice Information Processing Letter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)MATHGoogle Scholar
  2. 2.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)MATHGoogle Scholar
  3. 3.
    Albers, S., Hagerup, T.: Improved parallel integer sorting without concurrent writing. Information and Computation 136, 25–51 (1997)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Batcher, K.E.: Sorting networks and their applications. In: Proc. 1968 AFIPS Spring Joint Summer Computer Conference, pp. 307–314 (1968)Google Scholar
  5. 5.
    Chan, T.M.: All-pairs shortest paths with real weights in O(n 3/logn) time. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 318–324. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Dobosiewicz, W.: A more efficient algorithm for min-plus multiplication. Inter. J. Comput. Math. 32, 49–60 (1990)MATHCrossRefGoogle Scholar
  7. 7.
    Fredman, M.L.: New bounds on the complexity of the shortest path problem. SIAM J. Computing 5, 83–89 (1976)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fredman, M.L., Tarjan, R.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM 34, 596–615 (1987)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Galil, Z., Margalit, O.: All pairs shortest distances for graphs with small integer length edges. Information and Computation 134, 103–139 (1997)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Han, Y.: Improved algorithms for all pairs shortest paths. Information Processing Letters 91, 245–250 (2004)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Han, Y.: Achieving O(n 3/logn) time for all pairs shortest paths by using a smaller table. In: Proc. 21st Int. Conf. on Computers and Their Applications (CATA 2006), pp. 36–37 (2006)Google Scholar
  12. 12.
    Pettie, S.: A faster all-pairs shortest path algorithm for real-weighted sparse graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 85–97. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Pettie, S., Ramachandran, V.: A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput. 34(6), 1398–1431 (2005)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Sankowski, P.: Shortest paths in matrix multiplication time. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 770–778. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Seidel, R.: On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci. 51, 400–403 (1995)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Takaoka, T.: A new upper bound on the complexity of the all pairs shortest path problem. Information Processing Letters 43, 195–199 (1992)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Takaoka, T.: An O(n 3 loglogn/logn) time algorithm for the all-pairs shortest path problem. Information Processing Letters 96, 155–161 (2005)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Thorup, M.: Undirected single source shortest paths with positive integer weights in linear time. Journal of ACM 46(3), 362–394 (1999)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Yuster, R., Zwick, U.: Answering distance queries in directed graphs using fast matrix multiplication. In: 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 389–396. IEEE Comput. Soc., Los Alamitos (2005)CrossRefGoogle Scholar
  20. 20.
    Zwick, U.: All pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM 49(3), 289–317 (2002)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Zwick, U.: A slightly improved sub-cubic algorithm for the all pairs shortest paths problem. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 921–932. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yijie Han
    • 1
  1. 1.University of Missouri at Kansas CityKansas CityUSA

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