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arXiv · 2506.04246

Improving the average dilation of a metric graph by adding edges

Sariel Har-Peled·Eliot W. Robson
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Abstract

For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to augment $G$ with $k$ additional edges to reduce the maximum dilation. In this note, we consider a variant of this problem where the goal is to reduce the average dilation for pairs of points in $G$. We provide an $O(k)$ approximation algorithm for this problem, matching the approximation ratio given by prior work for the maximum dilation variant.

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Sariel Har-Peled, Eliot W. Robson. 2025-05-30. Improving the average dilation of a metric graph by adding edges. https://arxiv.org/abs/2506.04246

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