Self-stabilization and Byzantine Tolerance for Maximal Independent Set

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 from 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 $n$ is the number of nodes and $\Delta$ is the maximum degree of the network. Additionally, we present a modified version of this algorithm for anonymous systems under the adversarial distributed daemon that converges in $\mathcal O(n^{2})$ moves both in expected value and with high probability. Submission history Access Paper: View PDF HTML (experimental) TeX Source Additional Features Audio Summary Current browse context: References & Citations Google Scholar Semantic Scholar Bookmark Institution arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.