Computing the dilation of edge-augmented graphs in metric spaces

Authors:
Christian Wulff-Nilsen
Affiliations:
Department of Computer Science, University of Copenhagen, Copenhagen, Denmark
Venue:
Computational Geometry: Theory and Applications
Year:
2010

Citing 6
Cited 0

Finding the upper envelope of n line segments in O(n log n) time

Information Processing Letters
Algorithm 97: Shortest path

Communications of the ACM
Geometric Spanner Networks

Geometric Spanner Networks
More algorithms for all-pairs shortest paths in weighted graphs

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improving the Stretch Factor of a Geometric Network by Edge Augmentation

SIAM Journal on Computing
Computing Best and Worst Shortcuts of Graphs Embedded in Metric Spaces

ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how to improve the running time to O(n^3logn) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G@?{(u,v)} for every pair of distinct vertices u and v.