Greedy Completion for Weighted $(\hat{I}\pm ,{\hat{I}}^2)$-Spanners

Abstract

We study $(\hat{I}\pm ,{\hat{I}}^2)$-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.

ESA '26, 15 pages