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Simpler Computation of Single-Source Shortest Paths in Linear Average Time

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STACS 2004 (STACS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2996))

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Abstract

Meyer as well as Goldberg recently described algorithms that solve the single-source shortest-paths problem in linear average time on graphs with random edge lengths drawn from the uniform distribution on [0,1]. This note points out that the same result can be obtained through simple combinations of standard data structures and with a trivial probabilistic analysis.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs (1993)

    Google Scholar 

  2. Dantzig, G.B.: On the shortest route through a network. Management Sci. 6, 187–190 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34, 596–615 (1987)

    Article  MathSciNet  Google Scholar 

  5. Goldberg, V.: A simple shortest path algorithm with linear average time. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 230–241. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Hagerup, T., Rüb, C.: A guided tour of Chernoff bounds. Inform. Proc. Lett. 33, 305–308 (1990)

    Article  MATH  Google Scholar 

  7. Meyer, U.: Single-source shortest-paths on arbitrary directed graphs in linear average-case time. In: Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 797–806 (2001)

    Google Scholar 

  8. Meyer, U.: Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds. J. Algorithms 48, 91–134 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Thorup, M.: Integer priority queues with decrease key in constant time and the single source shortest paths problem. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC 2003), pp. 149–158 (2003)

    Google Scholar 

  10. Whiting, P.D., Hillier, J.A.: A method for finding the shortest route through a road network. Oper. Res. Quart. 11, 37–40 (1960)

    Article  Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Hagerup, T. (2004). Simpler Computation of Single-Source Shortest Paths in Linear Average Time. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_32

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  • DOI: https://doi.org/10.1007/978-3-540-24749-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21236-2

  • Online ISBN: 978-3-540-24749-4

  • eBook Packages: Springer Book Archive

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