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arXiv 2104.13499cs.DCcs.CG
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几何通信网络中的通信代价

Communication Costs in a Geometric Communication Network

Sima Hajiaghaei Shanjani, Valerie King

摘要:

通信网络是一个图,其中每个节点只具有关于图的局部信息,并且节点通过沿其边缘传递消息来进行通信。这里,我们考虑{ \it几何通信网络},其中节点也占据空间中的点,并且点之间的距离是欧几里得距离。我们的目标是了解在异步CONGEST KT 1模型中解决几个基本几何问题所需的通信成本,包括凸包、直径、最近对和这些问题的近似。这将Rajsbaum和Urrutia在2011年关于寻找平面几何通信网络的凸包的结果扩展到任意拓扑的网络。

英文摘要:

A communication network is a graph in which each node has only local information about the graph and nodes communicate by passing messages along its edges. Here, we consider the {\it geometric communication network} where the nodes also occupy points in space and the distance between points is the Euclidean distance. Our goal is to understand the communication cost needed to solve several fundamental geometry problems, including Convex Hull, Diameter, Closest Pair, and approximations of these problems, in the asynchronous CONGEST KT1 model. This extends the 2011 result of Rajsbaum and Urrutia for finding a convex hull of a planar geometric communication network to networks of arbitrary topology.

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。

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