认知无线电网络中的确定性盲重传
Deterministic Blind Rendezvous in Cognitive Radio Networks
摘要：
盲会合是认知无线电网络中的一个基本问题。这个问题涉及到一组代理（无线电），它们希望在没有共享基础设施的盲环境中发现彼此，并且它们最初不知道彼此。时间被划分为离散时隙;频谱被划分为离散信道，即$\{1,2,..., n\}$。每个代理可以在单个时隙中访问单个信道，并且我们说两个代理在相同时隙中访问相同信道时会合。模型是不对称的：每个代理$A_i$可以仅使用信道的特定子集$S_i$，并且不同的代理可以访问不同的信道子集。目标是为每个代理设计确定性的信道跳变调度，以保证具有重叠信道集的任何代理对之间的会合。两组独立的作者，Shin等人和Lin等人，分别给出了在$O(n^2)$和$O(n^3)$时间内保证异步盲会合的第一种构造。我们提出了一个大大改进的建设，保证任何两个代理，$A_i$，$A_j$，将会合在$O(|S_i| |S_j| \log\log n)$的时间。我们的结果是第一个实现非平凡的依赖$|S_i|$，可用通道的大小。这使我们，例如，以节省约二次因子超过最好的以前的结果在重要的情况下，当通道子集具有恒定的大小。我们还实现了最好的可能的约束的$O(1)$时间的对称情况下，以前的作品可以做得比$O(n)$。使用概率的方法和拉姆齐理论，我们提供的证据支持我们的怀疑，我们的建设是渐近最佳的小尺寸的通道子集：我们显示了$c |S_i||S_j|$下限和$c \log\log n$下限时，$|S_i|, |S_j| \leq n/2$。
英文摘要：
Blind rendezvous is a fundamental problem in cognitive radio networks. The problem involves a collection of agents (radios) that wish to discover each other in the blind setting where there is no shared infrastructure and they initially have no knowledge of each other. Time is divided into discrete slots; spectrum is divided into discrete channels, $\{1,2,..., n\}$. Each agent may access a single channel in a single time slot and we say that two agents rendezvous when they access the same channel in the same time slot. The model is asymmetric: each agent $A_i$ may only use a particular subset $S_i$ of the channels and different agents may have access to different subsets of channels. The goal is to design deterministic channel hopping schedules for each agent so as to guarantee rendezvous between any pair of agents with overlapping channel sets. Two independent sets of authors, Shin et al. and Lin et al., gave the first constructions guaranteeing asynchronous blind rendezvous in $O(n^2)$ and $O(n^3)$ time, respectively. We present a substantially improved construction guaranteeing that any two agents, $A_i$, $A_j$, will rendezvous in $O(|S_i| |S_j| \log\log n)$ time. Our results are the first that achieve nontrivial dependence on $|S_i|$, the size of the set of available channels. This allows us, for example, to save roughly a quadratic factor over the best previous results in the important case when channel subsets have constant size. We also achieve the best possible bound of $O(1)$ time for the symmetric situation; previous works could do no better than $O(n)$. Using the probabilistic method and Ramsey theory we provide evidence in support of our suspicion that our construction is asymptotically optimal for small size channel subsets: we show both a $c |S_i||S_j|$ lower bound and a $c \log\log n$ lower bound when $|S_i|, |S_j| \leq n/2$.
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。
