The Forgiving Graph: A distributed data structure for low stretch under adversarial attack

TL;DR

This paper introduces a distributed self-healing data structure called the Forgiving Graph, which maintains low stretch and bounded degree in peer-to-peer networks under adversarial node insertions and deletions.

Contribution

The paper presents a novel distributed algorithm that preserves network closeness and degree bounds despite adversarial attacks, with efficient repair mechanisms.

Findings

Maintains node distances within a logarithmic factor of the original under attacks.

Ensures node degrees do not increase by more than a factor of three.

Operates with low latency and bandwidth in a distributed setting.

Abstract

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick "repairs," which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes $v$ and $w$ whose distance would have been $\ell$ in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most $\ell \log n$ in the actual graph, where $n$ is the total number of vertices seen so far. Similarly, at any point, a node $v$ whose degree would have been $d$ in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our algorithm is completely distributed and has low latency and bandwidth requirements.