Easily repairable networks

TL;DR

This paper presents a new class of repairable distribution networks that withstand damage through repairability rather than redundancy, achieving optimal repair costs and hierarchical structures on lattice networks, and demonstrating resilience under repeated attacks.

Contribution

It introduces a novel class of repairable networks, proves a lower bound on repair costs, and extends results to networks resilient to repeated attacks.

Findings

Optimal repair cost bound established

Networks on square and triangular lattices achieve this bound

Networks can withstand unlimited attacks with modest repair cost increase

Abstract

We introduce a simple class of distribution networks which withstand damage by being repairable instead of redundant. We prove a lower bound for the expected cost of repair, and show that for networks on the square and triangular lattice, this bound is achievable and results in a network with exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks.