Local routing in a tree metric 1-spanner

Solomon and Elkin (SIAM J Discret Math 28(3):1173–1198, 2014) constructed a shortcutting scheme for weighted trees which results in 1-spanner the tree metric induced by input tree. The spanner has logarithmic lightness, diameter, linear number of edges bounded degree (provided degree). This been applied series papers devoted to designing degree, low-diameter, low-weight $$(1+\epsilon )$$ -spanners Euclidean doubling metrics. In this paper, we present simple local routing algorithm spanner. ratio 1, is guaranteed terminate after $$O(\log n)$$ hops requires $$O(\varDelta \log bits storage per vertex where $$\varDelta $$ maximum on constructed. can be adapted makes use scheme.