Self-Stabilizing Clock Synchronization in Dynamic Networks

Abstract

We consider the fundamental problem of clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually indicate the same value. Previous algorithms worked in static networks with drastic connectivity properties and assumed that global information is available at each agent. In this paper, we propose different solutions for time-varying topologies that require neither strong connectivity nor any global knowledge on the network. First, we study the case of unbounded clocks, and propose a self-stabilizing $MinMax$ algorithm that works if, in each sufficiently long but bounded period of time, there is an agent, called a root, that can send messages, possibly indirectly, to all other agents. Such networks are highly dynamic in the sense that roots may change arbitrarily over time. Moreover, the bound on the time required for achieving this rootedness property is unknown to the agents. Then we present a finite-state algorithm that synchronizes periodic clocks in dynamic networks that are strongly connected over bounded period of time. Here also, the bound on the time for achieving strong connectivity exists, but is not supposed to be known. Interestingly, our algorithm unifies several seemingly different algorithms proposed previously for static networks. Next, we show that strong connectivity is actually not required: our algorithm still works when the network is just rooted over bounded period of time with a set of roots that becomes stable. Finally, we study the time and space complexities of our algorithms, and discuss how initial timing information allows for more efficient solutions.