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Minimizing the Diameter of a Network Using Shortcut Edges

  • Erik D. Demaine
  • Morteza Zadimoghaddam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)

Abstract

We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constant-factor approximation algorithms for different variations of this problem. We also show how to improve the approximation ratios using resource augmentation to allow more than k shortcut edges. We observe a close relation between the single-source version of the problem, where we want to minimize the largest distance from a given source vertex, and the well-known k-median problem. First we show that our constant-factor approximation algorithms for the general case solve the single-source problem within a constant factor. Then, using a linear-programming formulation for the single-source version, we find a (1 + ε)-approximation using O(klogn) shortcut edges. To show the tightness of our result, we prove that any \(({3 \over 2}-\epsilon)\)-approximation for the single-source version must use Ω(klogn) shortcut edges assuming P ≠ NP.

Keywords

Approximation algorithms network design network repair 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Morteza Zadimoghaddam
    • 1
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA

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