Improving the Stretch Factor of a Geometric Network by Edge Augmentation

  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.},
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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