Self-stabilization and byzantine tolerance for maximal independent

TL;DR

This work tackles MIS construction under both transient and Byzantine faults in general networks using self-stabilizing randomized algorithms. It adapts a Byzantine-tolerant MIS approach under a fair distributed daemon, employing distance-based containment sets and degree-aware random candidacy to bound Byzantine impact, with convergence in $O(Δn)$ rounds w.h.p. on non-anonymous networks; it also provides an anonymous-system variant under an adversarial daemon with $O(n^{2})$ expected moves. The containment is formalized via sets $V_i$ defined by distance from Byzantine nodes, and legitimate configurations ensure MIS properties on the subgraph $V_2 ∪ I_\gamma$. Together, these results deliver the first known approach achieving self-stabilization and Byzantine tolerance under the fair daemon, plus a scalable anonymous solution under adversarial scheduling, with explicit convergence guarantees.

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 `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(Δn)$ rounds w.h.p., where $n$ and $Δ$ 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.

Figures (2)

• Figure 1: Execution
• Figure 2: What is the good containment radius?

Theorems & Definitions (24)

• Definition 1
• Definition 2
• Lemma 3
• Lemma 4
• Lemma 5
• Lemma 6
• Lemma 7
• Lemma 9
• Lemma 10
• Lemma 11