Self-Stabilization and Byzantine Tolerance for Maximal Independent Set

TL;DR

This paper presents a novel self-stabilizing algorithm that tolerates Byzantine faults for constructing a maximal independent set in networks, with proven convergence bounds under various fault models.

Contribution

It introduces the first algorithm capable of handling both transient and Byzantine faults for MIS construction under the fair distributed daemon.

Findings

Converges in O(Δn) rounds with high probability in general networks.

Modified version converges in O(n^2) expected steps for anonymous systems.

Provides bounds on Byzantine influence, excluding nodes near Byzantine faults.

Abstract

We analyze the impact of transient and Byzantine faults on the construction of a maximal independent set in a general network. We adapt the self-stabilizing algorithm presented by Turau \cite{turau2007linear} for computing such a vertex set. Our algorithm is self-stabilizing and also works under the more difficult context of arbitrary Byzantine faults. Byzantine nodes can prevent nodes close to them from taking part in the independent set for an arbitrarily long time. We give boundaries to their impact by focusing on the set of all nodes excluding nodes at distance 1 or less of Byzantine nodes, and excluding some of the nodes at distance 2. As far as we know, we present the first algorithm tolerating both transient and Byzantine faults under the fair distributed daemon. We prove that this algorithm converges in $ \mathcal O(\Delta n)$ rounds w.h.p., where $n$ and $\Delta$ are the size and the maximum degree of the network, resp. Additionally, we present a modified version of this algorithm for anonymous systems under the adversarial distributed daemon that converges in $ \mathcal O(n^{2})$ expected number of steps.