Greedy Completion for Weighted $(α,β)$-Spanners

Abstract: We study $(α,β)$-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 $\tilde{O}(n<sup>{1+1/k})$, which were previously unknown.