SINR模型中不知道坐标的稀释法
Achieving Dilution without Knowledge of Coordinates in the SINR Model
摘要：
针对无线电传输的SINR（Signal-to-Interference-plus-Noise-Ratio）模型中的各种基本分布式问题，已经开发了相当多的文献。通常研究的设置是当所有节点发送相同强度的信号时，并且每个设备仅能够访问关于网络中节点的总数$n$、每个节点的标签被取$[1,\dots,N]$的范围以及设备本身的标签的知识。此外，假设每个节点也知道其在欧几里得平面中的坐标。在本文中，我们创建了一种技术，允许算法设计者删除最后一个假设。关于节点的物理坐标的知识的不可用性的假设真正捕获了无线网络的“ad-hoc”性质。这一领域以前的工作使用了一种称为稀释的技术，其中节点以（预定的）循环方式进行传输，并且能够到达所有邻居。然而，在不知道物理坐标的情况下，不可能知道其包含（枢轴）网格框的坐标，并且似乎不可能使用稀释（以协调其传输）。我们提出了一种新的技术来实现稀释，而不使用物理坐标的知识。这种技术利用了这样的理解，即传输节点位于2-D空间中，由适当的枢轴网格分割，而不明确地参考这些节点的实际物理坐标。使用这种技术，只要任何物理网格盒中的发送节点的密度由已知常数限制，每个弱设备就可以在$Θ(\lg N)$轮中成功地将其消息发送到其所有邻居。这种技术，我们觉得，是一个重要的通用工具，用于设计实际的协议时，节点的物理坐标是未知的。
英文摘要：
Considerable literature has been developed for various fundamental distributed problems in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for radio transmission. A setting typically studied is when all nodes transmit a signal of the same strength, and each device only has access to knowledge about the total number of nodes in the network $n$, the range from which each node's label is taken $[1,\dots,N]$, and the label of the device itself. In addition, an assumption is made that each node also knows its coordinates in the Euclidean plane. In this paper, we create a technique which allows algorithm designers to remove that last assumption. The assumption about the unavailability of the knowledge of the physical coordinates of the nodes truly captures the `ad-hoc' nature of wireless networks. Previous work in this area uses a flavor of a technique called dilution, in which nodes transmit in a (predetermined) round-robin fashion, and are able to reach all their neighbors. However, without knowing the physical coordinates, it's not possible to know the coordinates of their containing (pivotal) grid box and seemingly not possible to use dilution (to coordinate their transmissions). We propose a new technique to achieve dilution without using the knowledge of physical coordinates. This technique exploits the understanding that the transmitting nodes lie in 2-D space, segmented by an appropriate pivotal grid, without explicitly referring to the actual physical coordinates of these nodes. Using this technique, it is possible for every weak device to successfully transmit its message to all of its neighbors in $Θ(\lg N)$ rounds, as long as the density of transmitting nodes in any physical grid box is bounded by a known constant. This technique, we feel, is an important generic tool for devising practical protocols when physical coordinates of the nodes are not known.
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