This paper studies the feasibility of reaching consensus in an anonymous dynamic network. In our model, $n$ anonymous nodes proceed in synchronous rounds. We adopt a hybrid fault model in which up to $f$ nodes may suffer crash or Byzantine faults, and the dynamic message adversary chooses a communication graph for each round. We introduce a stability property of the dynamic network -- $(T,D)$-dynaDegree for $T \geq 1$ and $n-1 \geq D \geq 1$ -- which requires that for every $T$ consecutive rounds, any fault-free node must have incoming directed links from at least $D$ distinct neighbors. These links might occur in different rounds during a $T$-round interval. $(1,n-1)$-dynaDegree means that the graph is a complete graph in every round. $(1,1)$-dynaDegree means that each node has at least one incoming neighbor in every round, but the set of incoming neighbor(s) at each node may change arbitrarily between rounds. We show that exact consensus is impossible even with $(1,n-2)$-dynaDegree. For an arbitrary $T$, we show that for crash-tolerant approximate consensus, $(T,\lfloor n/2 \rfloor)$-dynaDegree and $n > 2f$ are together necessary and sufficient, whereas for Byzantine approximate consensus, $(T,\lfloor (n+3f)/2 \rfloor)$-dynaDegree and $n > 5f$ are together necessary and sufficient.

翻译：本文研究了在匿名动态网络中达成共识的可行性。在我们的模型中，$n$个匿名节点在同步轮次中运行。我们采用混合故障模型，其中最多$f$个节点可能遭受崩溃或拜占庭故障，且动态消息对手为每一轮选择通信图。我们引入动态网络的一种稳定性属性——$(T,D)$-动态度（其中$T \geq 1$，$n-1 \geq D \geq 1$）——该属性要求：对于任意连续$T$轮，每个无故障节点必须至少从$D$个不同邻居接收有向链路。这些链路可能出现在$T$轮区间内的不同轮次中。$(1,n-1)$-动态度表示每轮通信图均为完全图。$(1,1)$-动态度表示每轮每个节点至少有一个入邻居，但各节点的入邻居集合可在轮次间任意变化。我们证明，即使满足$(1,n-2)$-动态度，精确共识也无法实现。对于任意$T$，我们证明：在崩溃容忍的近似共识中，$(T,\lfloor n/2 \rfloor)$-动态度与$n > 2f$共同构成充要条件；而在拜占庭容忍的近似共识中，$(T,\lfloor (n+3f)/2 \rfloor)$-动态度与$n > 5f$共同构成充要条件。