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arXiv · 2603.17047

Greedy Completion for Weighted $(\alpha,\beta)$-Spanners

Elad Tzalik
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Abstract

We study $(\alpha,\beta)$-spanners for weighted graphs. We propose a simple greedy completion procedure which starts from a sparse initial graph, and repeatedly fixes pairs of vertices with a bad stretch, generalizing Knudsen's additive completion [SWAT '14]. As an application, we construct $(k,k-1)$-spanners for weighted graphs of size $\tilde{O}(n^{1+1/k})$, which were previously unknown.

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Elad Tzalik. 2026-03-17. Greedy Completion for Weighted $(\alpha,\beta)$-Spanners. https://arxiv.org/abs/2603.17047

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