A Simple Linear Time Algorithm for Computing a (2k — 1)-Spanner of O(n1+1/k) Size in Weighted Graphs

  • Surender Baswana
  • Sandeep Sen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)


Let G(V,E) be an undirected weighted graph with |V| = n, and |E| = m. A t-spanner of the graph G(V,E) is a sub-graph G(V,ES) such that the distance between any pair of vertices in the spanner is at most t times the distance between the two in the given graph. A 1963 girth conjecture of Erdős implies that Ω(n1+1/k) edges are required in the worst case for any (2k − 1)-spanner, which has been proved for k = 1, 2, 3, 5. There exist polynomial time algorithms that can construct spanners with the size that matches this conjectured lower bound, and the best known algorithm takes O(mn1/k) expected running time. In this paper, we present an extremely simple linear time randomized algorithm that constructs (2k − 1)-spanner of size matching the conjectured lower bound.

Our algorithm requires local information for computing a spanner, and thus can be adapted suitably to obtain efficient distributed and parallel algorithms.


Graph algorithms Randomized algorithms Shortest path 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Surender Baswana
    • 1
  • Sandeep Sen
    • 1
  1. 1.Department of Computer Science and EngineeringI.I.T. DelhiNew DelhiIndia

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