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All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

We describe an O(n 3/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (1976), Takaoka (1992), Dobosiewicz (1990), Han (2004), Takaoka (2004), and Zwick (2004). The new algorithm is surprisingly simple and different from previous ones.

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References

  1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)

    MATH  Google Scholar 

  2. Alon, N., Galil, Z., Margalit, O.: On the exponent of the all pairs shortest path problem. J. Comput. Sys. Sci. 54, 255–262 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arlazarov, V.L., Dinic, E.C., Kronrod, M.A., Faradzev, I.A.: On economical construction of the transitive closure of a directed graph. Soviet Math. Dokl. 11, 1209–1210 (1970)

    MATH  Google Scholar 

  4. Buchsbaum, A.L., Kaplan, H., Rogers, A., Westbrook, J.R.: Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators. In: Proc. 30th ACM Sympos. Theory Comput., pp. 279–288 (1998)

    Google Scholar 

  5. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symbolic Comput. 9, 251–280 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. McGraw-Hill, New York (2001)

    MATH  Google Scholar 

  7. Dobosiewicz, W.: A more efficient algorithm for the min-plus multiplication. Int. J. Computer Math. 32, 49–60 (1990)

    Article  MATH  Google Scholar 

  8. Eppstein, D.: Quasiconvex analysis of backtracking algorithms. In: Proc. 15th ACM-SIAM Sympos. Discrete Algorithms, pp. 788–797 (2004)

    Google Scholar 

  9. Feder, T., Motwani, R.: Clique partitions, graph compression and speeding-up algorithms. J. Comput. Sys. Sci. 51, 261–272 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fredman, M.L.: New bounds on the complexity of the shortest path problem. SIAM J. Comput. 5, 49–60 (1976)

    Article  MathSciNet  Google Scholar 

  11. Galil, Z., Margalit, O.: All pairs shortest paths for graphs with small integer length edges. J. Comput. Sys. Sci. 54, 243–254 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Han, Y.: Improved algorithm for all pairs shortest paths. Inform. Process. Lett. 91, 245–250 (2004)

    Article  MathSciNet  Google Scholar 

  13. Pettie, S.: A new approach to all-pairs shortest paths on real-weighted graphs. Theoret. Comput. Sci. 312, 47–74 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Pettie, S., Ramachandran, V.: A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput. (to appear)

    Google Scholar 

  15. Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, New York (1985)

    Google Scholar 

  16. Seidel, R.: On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Sys. Sci. 51, 400–403 (1995)

    Article  MathSciNet  Google Scholar 

  17. Shoshan, A., Zwick, U.: All pairs shortest paths in undirected graphs with integer weights. In: Proc. 40th IEEE Sympos. Found. Comput. Sci., pp. 605–614 (1999)

    Google Scholar 

  18. Strassen, V.: Gaussian elimination is not optimal. Numerische Mathematik 13, 354–356 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  19. Takaoka, T.: A new upper bound on the complexity of the all pairs shortest path problem. Inform. Process. Lett. 43, 195–199 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Takaoka, T.: A faster algorithm for the all-pairs shortest path problem and its application. In: Chwa, K.-Y., Munro, J.I.J. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 278–289. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  21. Yuster, R., Zwick, U.: Fast sparse matrix multiplication. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 604–615. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. Zwick, U.: All-pairs shortest paths using bridging sets and rectangular matrix multiplication. J. ACM 49, 289–317 (2002)

    Article  MathSciNet  Google Scholar 

  23. Zwick, U.: A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 921–932. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Chan, T.M. (2005). All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_28

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  • DOI: https://doi.org/10.1007/11534273_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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