Affiliation:
1. University of Sydney, Camperdown NSW, Australia
Abstract
Most of the literature on spanners focuses on building the graph from scratch. This article instead focuses on adding edges to improve an existing graph. A major open problem in this field is: Given a graph embedded in a metric space, and a budget of
k
edges, which
k
edges do we add to produce a minimum-dilation graph? The special case where
k=1
has been studied in the past, but no major breakthroughs have been made for
k > 1
. We provide the first positive result, an
O(k)
-approximation algorithm that runs in
O(n
3
log
n
) time.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Reference21 articles.
1. DILATION-OPTIMAL EDGE DELETION IN POLYGONAL CYCLES
2. Sparse geometric graphs with small dilation
3. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
4. Hubert T.-H. Chan, Anupam Gupta, Bruce M. Maggs, and Shuheng Zhou. 2005. On hierarchical routing in doubling metrics. In Proceedings of the 16th Annual Symposium on Discrete Algorithms. SIAM, 762–771. Retrieved from http://dl.acm.org/citation.cfm?id=1070432.1070540
5. Spanning Trees and Spanners