A Self-stabilizing Link-Coloring Protocol Resilient to Byzantine Faults in Tree Networks

Self-stabilizing protocols can tolerate any type and any number of transient faults. But self-stabilizing protocols have no guarantee of their behavior against permanent faults. Thus, investigation concerning self-stabilizing protocols resilient to permanent faults is important. This paper proposes a self-stabilizing link-coloring protocol resilient to (permanent) Byzantine faults in tree networks. The protocol assumes the central daemon, and uses Δ+1 colors where Δ is the maximum degree in the network. This protocol guarantees that, for any nonfaulty process v, if the distance from v to any Byzantine ancestor of v is greater than two, v reaches its desired states within three rounds and never changes its states after that. Thus, it achieves fault containment with radius of two. Moreover, we prove that the containment radius becomes Ω(log n) when we use only Δ colors, and prove that the containment radius becomes Ω(n) under the distributed daemon. These lower bound results prove necessity of Δ+1 colors and the central daemon to achieve fault containment with a constant radius.