匿名未知动态网络中的计数与认证
Naming and Counting in Anonymous Unknown Dynamic Networks
摘要：
在这项工作中，我们研究的基本命名和计数问题（和一些变化）的网络是匿名的，未知的，并可能是动态的。在计数时，节点必须确定网络的大小n，在命名时，它们必须以唯一的身份结束。匿名的意思是所有节点都从相同的状态开始，可能除了一个唯一的领导节点，未知的是节点没有网络的先验知识（除了必要时的一些最小知识），包括对n的无知。网络动态性由1-区间连通性模型建模，其中通信是同步的，并且最坏情况下的对手选择每个轮的边缘，条件是每个实例都是连通的。我们首先专注于静态网络与广播，我们证明，如果没有一个领导者，计数是不可能解决的，命名是不可能解决的，即使有一个领导者，即使节点知道n。这些不可能性也会延续到动态网络中。我们还表明，一个独特的领导人足以解决线性时间计数。然后，我们专注于动态网络与广播。我们猜想，动态性使非平凡的计算不可能。鉴于此，我们让节点知道最大度的上界，并表明在这种情况下，节点可以获得n的上界。最后，我们将广播替换为一对一，其中节点可以向其每个邻居发送不同的消息。有趣的是，这种自然变化被证明在计算上等同于全知识模型，其中存在唯一的名称并且网络的大小是已知的。
英文摘要：
In this work, we study the fundamental naming and counting problems (and some variations) in networks that are anonymous, unknown, and possibly dynamic. In counting, nodes must determine the size of the network n and in naming they must end up with unique identities. By anonymous we mean that all nodes begin from identical states apart possibly from a unique leader node and by unknown that nodes have no a priori knowledge of the network (apart from some minimal knowledge when necessary) including ignorance of n. Network dynamicity is modeled by the 1-interval connectivity model, in which communication is synchronous and a worst-case adversary chooses the edges of every round subject to the condition that each instance is connected. We first focus on static networks with broadcast where we prove that, without a leader, counting is impossible to solve and that naming is impossible to solve even with a leader and even if nodes know n. These impossibilities carry over to dynamic networks as well. We also show that a unique leader suffices in order to solve counting in linear time. Then we focus on dynamic networks with broadcast. We conjecture that dynamicity renders nontrivial computation impossible. In view of this, we let the nodes know an upper bound on the maximum degree that will ever appear and show that in this case the nodes can obtain an upper bound on n. Finally, we replace broadcast with one-to-each, in which a node may send a different message to each of its neighbors. Interestingly, this natural variation is proved to be computationally equivalent to a full-knowledge model, in which unique names exist and the size of the network is known.
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