向互连网络添加仲裁人：一轮中可以（不可以）计算什么
Adding a referee to an interconnection network: What can(not) be computed in one round
摘要：
在本文中，我们问的分布式网络的属性可以计算从它的节点提供的少量的本地信息。我们考虑的分布式模型是经典的CONGEST（分布式）模型的一个限制，它接近Babai，Kimmel和Lokam定义的同时消息（通信复杂性）模型。更准确地说，这n个节点中的每一个节点（只知道自己的ID和邻居的ID）都可以向某个中心实体（称为裁判）发送O（log n）位的消息。裁判员有可能决定网络拓扑G的一些基本结构性质吗？我们证明了简单的问题，比如“G包含平方吗？“，“G包含三角形吗？或“G的直径至多为3吗？一般不能解决。另一方面，裁判可以解码的消息，以便有充分的知识G时，G属于许多图类，如平面图，有界树宽图，更一般地说，有界退化图。我们留下开放的问题有关的连通性的任意图。
英文摘要：
In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close to the simultaneous messages (communication complexity) model defined by Babai, Kimmel and Lokam. More precisely, each of these n nodes -which only knows its own ID and the IDs of its neighbors- is allowed to send a message of O(log n) bits to some central entity, called the referee. Is it possible for the referee to decide some basic structural properties of the network topology G? We show that simple questions like, "does G contain a square?", "does G contain a triangle?" or "Is the diameter of G at most 3? cannot be solved in general. On the other hand, the referee can decode the messages in order to have full knowledge of G when G belongs to many graph classes such as planar graphs, bounded treewidth graphs and, more generally, bounded degeneracy graphs. We leave open questions related to the connectivity of arbitrary graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
