Light Spanners with Small Hop-Diameter
Sujoy Bhore, Lazar Milenkovic

TL;DR
This paper introduces a new framework for constructing light geometric spanners with small hop-diameter, achieving optimal tradeoffs between lightness and hop-diameter across various metric spaces, including doubling metrics.
Contribution
The authors develop a tree cover-based framework that generalizes and tightens the tradeoff between lightness and hop-diameter for geometric spanners.
Findings
Framework based on tree covers for spanner construction
Achieves tight tradeoff between lightness and hop-diameter
Applicable to doubling metrics and general metric spaces
Abstract
Lightness, sparsity, and hop-diameter are the fundamental parameters of geometric spanners. Arya et al. [STOC'95] showed in their seminal work that there exists a construction of Euclidean -spanners with hop-diameter and lightness . They also gave a general tradeoff of hop-diameter and sparsity , where is a very slowly growing inverse of an Ackermann-style function. The former combination of logarithmic hop-diameter and lightness is optimal due to the lower bound by Dinitz et al. [FOCS'08]. Later, Elkin and Solomon [STOC'13] generalized the light spanner construction to doubling metrics and extended the tradeoff for more values of hop-diameter . In a recent line of work [SoCG'22, SoCG'23], Le et al. proved that the aforementioned tradeoff between the hop-diameter and sparsity is tight for every choice of…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
