Reliable Spanners for Metric Spaces

TL;DR

This paper introduces new constructions of reliable spanners that maintain network properties despite large failures, applicable to various metric spaces including planar graphs and trees.

Contribution

It extends reliable spanner constructions from Euclidean spaces to planar graphs, trees, and general metric spaces, broadening their applicability.

Findings

Reliable spanners can withstand large node failures with minimal damage.

New constructions are near linear in size for various metric spaces.

The approach generalizes previous Euclidean-based methods.

Abstract

A spanner is reliable if it can withstand large, catastrophic failures in the network. More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation, that is, the spanner property is maintained for almost all nodes in the residual graph. Constructions of reliable spanners of near linear size are known in the low-dimensional Euclidean settings. Here, we present new constructions of reliable spanners for planar graphs, trees and (general) metric spaces.