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

arXiv:2603.17047v1 Announce Type: new
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 Kunedsen’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.