arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 1712.03053cs.NI
收藏

以近乎恒定的速率进行无线聚合

Wireless Aggregation at Nearly Constant Rate

Magnus M. Halldorsson, Tigran Tonoyan

摘要:

传感器网络中最基本的任务之一是计算输入测量的(可压缩)聚合函数。通过适当地选择聚合树、树边缘的TDMA调度和传输功率,可以保持什么样的计算速率?这可以被看作是无线网络的汇聚广播容量。我们在这里表明,最优速率实际上是一个常数。这甚至在干扰的物理模型下在\emph{arbitrary}网络中也成立。这与以前的对数界限(例如,$Ω(1/\log n)$)。也就是说,我们表明,$Ω(1/\log^* Δ)$的速率是可能的,其中$Δ$是长度多样性(节点之间的最远距离与最短距离之间的比率)。这也意味着无线连接的\emph{scheduling complexity}是$O(\log^* Δ)$。这是使用自然最小生成树(MST)实现的。我们的方法关键取决于选择适当的功率分配的情况下,因为没有功率控制,只能保证一个平凡的线性速率。我们还表明,有一个固定的功率分配,允许速率为$Ω(1/\log\log Δ)$。令人惊讶的是,这些边界是最好的可能。没有聚合网络可以保证比使用固定功率分配的$O(1/\log\log Δ)$更好的速率。而且,当使用任意功率控制时,存在其MST不能在少于$Ω(1/\log^* Δ)$的时隙中被调度的实例。

英文摘要:

One of the most fundamental tasks in sensor networks is the computation of a (compressible) aggregation function of the input measurements. What rate of computation can be maintained, by properly choosing the aggregation tree, the TDMA schedule of the tree edges, and the transmission powers? This can be viewed as the convergecast capacity of a wireless network. We show here that the optimal rate is effectively a constant. This holds even in \emph{arbitrary} networks, under the physical model of interference. This compares with previous bounds that are logarithmic (e.g., $Ω(1/\log n)$). Namely, we show that a rate of $Ω(1/\log^* Δ)$ is possible, where $Δ$ is the length diversity (ratio between the furthest to the shortest distance between nodes). It also implies that the \emph{scheduling complexity} of wireless connectivity is $O(\log^* Δ)$. This is achieved using the natural minimum spanning tree (MST). Our method crucially depends on choosing the appropriate power assignment for the instance at hand, since without power control, only a trivial linear rate can be guaranteed. We also show that there is a fixed power assignment that allows for a rate of $Ω(1/\log\log Δ)$. Surprisingly, these bounds are best possible. No aggregation network can guarantee a rate better than $O(1/\log\log Δ)$ using fixed power assignment. Also, when using arbitrary power control, there are instances whose MSTs cannot be scheduled in fewer than $Ω(1/\log^* Δ)$ slots.

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。

↑