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A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs

  • Seth Pettie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)

Abstract

We present a faster all-pairs shortest paths algorithm for arbitrary real-weighted directed graphs. The algorithm works in the fundamental comparison- addition model and runs in O(mn+n 2 log log n) time, where m and n are the number of edges & vertices, respectively. This is strictly faster than Johnson’s algorithm (for arbitrary edge-weights) and Dijkstra’s algorithm (for positive edge-weights) when m = o(n log n) and matches the running time of Hagerup’s APSP algorithm, which assumes integer edge-weights and a more powerful model of computation.

Keywords

Short Path Edge Length Short Path Problem Short Path Algorithm Normalize Edge Length 
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. [CLR90]
    T. Cormen, C. Leiserson, R. Rivest. Intro. to Algorithms. MIT Press, 1990.Google Scholar
  2. [Dij59]
    E. W. Dijkstra. A note on two problems in connexion with graphs. In Numer. Math., 1 (1959), 269–271.MATHCrossRefMathSciNetGoogle Scholar
  3. [FT87]
    M. L. Fredman, R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. In JACM 34 (1987), 596–615.CrossRefMathSciNetGoogle Scholar
  4. [G85]
    H. N. Gabow. A scaling algorithm for weighted matching on general graphs. In Proc. FOCS 1985, 90–99.Google Scholar
  5. [Hag00]
    T. Hagerup. Improved shortest paths on the word RAM. In Proc. ICALP 2000, LNCS volume 1853, 61–72.Google Scholar
  6. [J77]
    D. B. Johnson. Efficient algorithms for shortest paths in sparse networks. J. Assoc. Comput. Mach. 24 (1977), 1–13.MATHMathSciNetGoogle Scholar
  7. [Pet02]
    S. Pettie. A faster all-pairs shortest path algorithm for real-weighted sparse graphs. UTCS Technical Report CS-TR-02-13, February, 2002.Google Scholar
  8. [Pet02b]
    S. Pettie. On the comparison-addition complexity of all-pairs shortest paths. UTCS Technical Report CS-TR-02-21, April, 2002.Google Scholar
  9. [PRS02]
    S. Pettie, V. Ramachandran, S. Sridhar. Experimental evaluation of a new shortest path algorithm. Proceedings of ALENEX 2002.Google Scholar
  10. [PR02]
    S. Pettie, V. Ramachandran. Computing shortest paths with comparisons and additions. Proceedings of SODA 2002, 267–276.Google Scholar
  11. [Tar79]
    R. E. Tarjan. A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. Syst. Sci. 18 (1979), no. 2, 110–127.MATHCrossRefMathSciNetGoogle Scholar
  12. [Tho99]
    M. Thorup. Undirected single source shortest paths with positive integer weights in linear time. J. Assoc. Comput. Mach. 46 (1999), no. 3, 362–394.MATHMathSciNetGoogle Scholar
  13. [vEKZ77]
    P. van Emde Boas, R. Kaas, E. Zijlstra. Design and implementation of an efficient priority queue. Math. Syst. Theory 10 (1977), 99–127.MATHCrossRefGoogle Scholar
  14. [Z01]
    U. Zwick. Exact and approximate distances in graphs-A survey. Updated version at http://www.cs.tau.ac.il/zwick/, Proc. of 9th ESA (2001), 33–48.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Seth Pettie
    • 1
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustin

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