Light, Reliable Spanners
Arnold Filtser, Yuval Gitlitz, Ofer Neiman

TL;DR
This paper introduces the concept of light, reliable spanners in metric spaces, using randomness to achieve low-weight structures that preserve distances despite failures, with near-optimal parameters for various metric types.
Contribution
It develops oblivious reliable spanners with provably optimal lightness bounds, especially for $k$-HSTs and doubling metrics, advancing the understanding of fault-tolerant spanner constructions.
Findings
Oblivious $ u$-reliable $(2+2/(k-1))$-spanner for $k$-HST with $ ilde{O}( u^{-2})$ lightness.
Matching lower bounds show $ u^{-2}$ is tight for lightness.
For doubling metrics, achieves near-optimal reliable spanners with $ ilde{O}( u^{-2})$ lightness.
Abstract
A \emph{-reliable spanner} of a metric space , is a (dominating) graph , such that for any possible failure set , there is a set just slightly larger , and all distances between pairs in are (approximately) preserved in . Recently, there have been several works on sparse reliable spanners in various settings, but so far, the weight of such spanners has not been analyzed at all. In this work, we initiate the study of \emph{light} reliable spanners, whose weight is proportional to that of the Minimum Spanning Tree (MST) of . We first observe that unlike sparsity, the lightness of any deterministic reliable spanner is huge, even for the metric of the simple path graph. Therefore, randomness must be used: an \emph{oblivious} reliable spanner is a distribution over spanners, and the bound on…
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