In the stabilizing consensus problem each agent of a networked system has an input value and is repeatedly writing an output value; it is required that eventually all the output values stabilize to the same value which, moreover, must be one of the input values. We study this problem for a synchronous model with identical and anonymous agents that are connected by a time-varying topology and may join the system at any time (asynchronous start). Our main result is a generic MinMax algorithm that solves the stabilizing consensus problem in this model when, 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. We stress that the bound on the time required for achieving this rootedness property is unknown to the agents. Such topologies are highly dynamic (in particular, roots may change arbitrarily over time) and may have very weak connectivity properties (an agent may be never a root). Our distributed MinMax algorithms thus require neither central control nor any global information and are also quite efficient in terms of message size and storage requirements.

在稳定共识问题中，网络系统的每个代理程序都有一个输入值，并且正在重复写入一个输出值。最终要求所有输出值都稳定到相同的值，而且该值必须是输入值之一。我们针对具有相同和匿名代理的同步模型研究此问题，这些代理通过时变拓扑连接并且可以随时加入系统（异步启动）。我们的主要结果是一种通用的MinMax算法，该算法解决了该模型中的稳定共识问题，即在每个足够长的有限时间内，都有一个称为根的代理，可以间接向所有其他代理发送消息。我们强调，实现这种生根性所需的时间界限对于代理人是未知的。这样的拓扑是高度动态的（特别是根可以随时间任意变化），并且连接性能很弱（代理可能永远不会是根）。因此，我们的分布式MinMax算法既不需要中央控制，也不需要任何全局信息，并且在消息大小和存储要求方面也非常有效。