Improving the Stretch Factor of a Geometric Network by Edge Augmentation

@article{Farshi2008ImprovingTS,
  title={Improving the Stretch Factor of a Geometric Network by Edge Augmentation},
  author={Mohammad Farshi and Panos Giannopoulos and Joachim Gudmundsson},
  journal={SIAM J. Comput.},
  year={2008},
  volume={38},
  pages={226-240}
}
Given a Euclidean graph G in Rd with n vertices and m edges, we consider the problem of adding an edge to G such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a graph with positive edge weights runs in O(nm+n2 logn) time, resulting in a trivial O(n3m+n4 logn)-time algorithm for computing the optimal edge. First, we show that a simple modification yields the optimal solution in O(n4) time using O(n2) space. To… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 40 references

Geometric Spanner Networks

  • G. Narasimhan, M. Smid
  • Cambridge University Press, Cambridge, UK
  • 2007
Highly Influential
4 Excerpts

Geometric Spanner Networks: Open Problems

  • G. Narasimhan
  • Invited talk at the 1st Utrecht- Carleton…
  • 2002
Highly Influential
5 Excerpts

Tightness of Upper Bound on tB/tP

  • A. Grüne
  • MANUSCRIPT
  • 2005
1 Excerpt

( 1 +  , β ) - spanner constructions for general graphs

  • A. Proskurowski, D. Zappala, K. J. Windisch
  • SIAM J . Comput .
  • 2004

( 1 + 2 , β )spanner constructions for general graphs

  • D. Peleg.
  • SIAM Journal on Computing
  • 2004

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