Shortest Paths in Planar Graphs with Real Lengths in O(nlog2n/loglogn) Time

  • Shay Mozes
  • Christian Wulff-Nilsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6347)


Given an n-vertex planar directed graph with real edge lengths and with no negative cycles, we show how to compute single-source shortest path distances in the graph in O(nlog2n/loglogn) time with O(n) space. This improves on a recent O(nlog2n) time bound by Klein et al.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chambers, E.W., Erickson, J., Nayyeri, A.: Homology flows, cohomology cuts. In: Proc. 42nd Ann. ACM Symp. Theory Comput., pp. 273–282 (2009)Google Scholar
  2. 2.
    Erickson, J.: Private Communication (2010)Google Scholar
  3. 3.
    Fakcharoenphol, J., Rao, S.: Planar graphs, negative weight edges, shortest paths, and near linear time. J. Comput. Syst. Sci. 72(5), 868–889 (2006)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Henzinger, M.R., Klein, P.N., Rao, S., Subramanian, S.: Faster shortest-path algorithms for planar graphs. J. Comput. Syst. Sci. 55(1), 3–23 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Klawe, M.M., Kleitman, D.J.: An almost linear time algorithm for generalized matrix searching. SIAM Journal on Discrete Math. 3(1), 81–97 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Klein, P.N.: Multiple-source shortest paths in planar graphs. In: Proceedings, 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 146–155 (2005)Google Scholar
  7. 7.
    Klein, P.N., Mozes, S., Weimann, O.: Shortest Paths in Directed Planar Graphs with Negative Lengths: a Linear-Space O(nlog2n)-Time Algorithm. In: Proc. 19th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 236–245 (2009)Google Scholar
  8. 8.
    Lipton, R.J., Rose, D.J., Tarjan, R.E.: Generalized nested dissection. SIAM Journal on Numerical Analysis 16, 346–358 (1979)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Miller, G.L.: Finding small simple cycle separators for 2-connected planar graphs. J. Comput. Syst. Sci. 32, 265–279 (1986)MATHCrossRefGoogle Scholar
  10. 10.
    Aggarwal, A., Klawe, M., Moran, S., Shor, P.W., Wilber, R.: Geometric applications of a matrix searching algorithm. In: SCG 1986: Proceedings of the second annual symposium on Computational geometry, pp. 285–292 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Shay Mozes
    • 1
  • Christian Wulff-Nilsen
    • 2
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

Personalised recommendations