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arXiv · 2007.12350

Improving the dilation of a metric graph by adding edges

Joachim Gudmundsson·Sampson Wong
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Abstract

Most of the literature on spanners focuses on building the graph from scratch. This paper 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.

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Joachim Gudmundsson, Sampson Wong. 2020-07-24. Improving the dilation of a metric graph by adding edges. https://arxiv.org/abs/2007.12350

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