A Simple Linear Time Algorithm for Computing a (2k — 1)Spanner of O (n ^{1+1/k } ) Size in Weighted Graphs
 Surender Baswana,
 Sandeep Sen
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Abstract
Let G(V,E) be an undirected weighted graph with V = n, and E = m. A tspanner of the graph G(V,E) is a subgraph G(V,E _{S}) 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(n ^{1+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(mn ^{1/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.
 Title
 A Simple Linear Time Algorithm for Computing a (2k — 1)Spanner of O(n ^{1+1/k }) Size in Weighted Graphs
 Book Title
 Automata, Languages and Programming
 Book Subtitle
 30th International Colloquium, ICALP 2003 Eindhoven, The Netherlands, June 30 – July 4, 2003 Proceedings
 Pages
 pp 384396
 Copyright
 2003
 DOI
 10.1007/3540450610_32
 Print ISBN
 9783540404934
 Online ISBN
 9783540450610
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2719
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Graph algorithms
 Randomized algorithms
 Shortest path
 Industry Sectors
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 Editors

 Jos C. M. Baeten ^{(1)}
 Jan Karel Lenstra ^{(2)}
 Joachim Parrow ^{(3)}
 Gerhard J. Woeginger ^{(4)}
 Editor Affiliations

 1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven
 2. School of Industrial and Systems Engineering, Georgia Institute of Technology
 3. Department of Information Technology, Uppsala University
 4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente
 Authors

 Surender Baswana ^{(5)}
 Sandeep Sen ^{(5)}
 Author Affiliations

 5. Department of Computer Science and Engineering, I.I.T. Delhi, Hauz Khas, New Delhi, 110016, India
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