Exploring the Limits of Static Failover Routing

TL;DR

This paper investigates the fundamental limits of static, destination-based routing schemes' resilience to edge failures, exploring various models and establishing conditions under which reliable delivery can be guaranteed.

Contribution

It systematically analyzes the Static-Routing-Resiliency problem across multiple models, providing both positive and negative results linking graph connectivity to routing resilience.

Findings

Resiliency depends on the graph's edge-connectivity.

Certain models guarantee delivery up to specific failure thresholds.

Some configurations cannot ensure delivery beyond minimal connectivity.

Abstract

We present and study the Static-Routing-Resiliency problem, motivated by routing on the Internet: Given a graph $G$, a unique destination vertex $d$, and an integer constant $c>0$, does there exist a static and destination-based routing scheme such that the correct delivery of packets from any source $s$ to the destination $d$ is guaranteed so long as (1) no more than $c$ edges fail and (2) there exists a physical path from $s$ to $d$? We embark upon a systematic exploration of this fundamental question in a variety of models (deterministic routing, randomized routing, with packet-duplication, with packet-header-rewriting) and present both positive and negative results that relate the edge-connectivity of a graph, i.e., the minimum number of edges whose deletion partitions $G$, to its resiliency.