# Name Independent Fault Tolerant Routing Scheme

## TL;DR

This paper introduces a new name-independent fault-tolerant routing scheme capable of handling multiple edge faults in undirected weighted graphs, with efficient stretch and memory usage, improving network reliability without node naming constraints.

## Contribution

The paper presents a novel construction method for name-independent fault-tolerant routing schemes, including schemes for multiple faults and specialized schemes for single or double faults, with explicit bounds on stretch and memory.

## Key findings

- Handles any set of forbidden edges with |F|+1 connected graphs
- Achieves stretch of O(k^2 |F|^3 (|F|+log^2 n) log D)
- Uses compact routing tables of size ~O(k n^{1/k}(k + deg(v))) bits

## Abstract

We consider the problem of routing in presence of faults in undirected weighted graphs. More specifically, we focus on the design of compact name-independent fault-tolerant routing schemes, where the designer of the scheme is not allowed to assign names to nodes, i.e., the name of a node is just its identifier. Given a set $F$ of faulty (or forbidden) edges, the goal is to route from a source node $s$ to a target $t$ avoiding the forbidden edges in $F$. Given any name-dependent fault-tolerant routing scheme and any name-independent routing scheme, we show how to use them as a black box to construct a name-independent fault-tolerant routing scheme. In particular, we present a name-independent routing scheme able to handle any set $F$ of forbidden edges in $|F|+1$ connected graphs. This has stretch $O(k^2\,|F|^3(|F|+\log^2 n)\log D)$, where $D$ is the diameter of the graph. It uses tables of size $ \widetilde{O}(k\, n^{1/k}(k + deg(v)))$ bits at every node $v$, where $deg(v)$ is the degree of node $v$. In the context of networks that suffer only from occasional failures, we present a name-independent routing scheme that handles only $1$ fault at a time, and another routing scheme that handles at most $2$ faults at a time. The former uses $\widetilde{O}(k^2\, n^{1/k} + k\,deg(v))$ bits of memory per node, with stretch $O(k^3\log D)$. The latter consumes in average $ \widetilde{O}(k^2 \,n^{1/k} + deg(v))$ bits of memory per node, with stretch $O(k^2\log D)$.

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Source: https://tomesphere.com/paper/1704.06078