无线电网络容量的一个界
A Bound on the Throughput of Radio Networks
摘要：
我们认为，研究的无线电网络模型：一个同步模型的图形G=（V，E）与|V| =n，其中在每一轮，每个节点要么发送一个数据包，长度B=欧米茄（log n）位，或监听。每个节点接收一个数据包，如果它正在监听，并且恰好有一个邻居正在发送。我们考虑k-消息广播的问题，其中k个消息，每个消息具有Theta（B）比特，被放置在图的任意节点中，目标是将所有消息传递到所有节点。我们提出了一个简单的证明，表明存在一个半径为2的无线电网络，对于任何k，广播k消息需要至少欧米茄（k log n）轮。也就是说，在这个网络中，不管算法如何，最大可实现的广播吞吐量是O（1/log n）。
英文摘要：
We consider the well-studied radio network model: a synchronous model with a graph G=(V,E) with |V|=n where in each round, each node either transmits a packet, with length B=Omega(log n) bits, or listens. Each node receives a packet iff it is listening and exactly one of its neighbors is transmitting. We consider the problem of k-message broadcast, where k messages, each with Theta(B) bits, are placed in an arbitrary nodes of the graph and the goal is to deliver all messages to all the nodes. We present a simple proof showing that there exist a radio network with radius 2 where for any k, broadcasting k messages requires at least Omega(k log n) rounds. That is, in this network, regardless of the algorithm, the maximum achievable broadcast throughput is O(1/log n).
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。
