确定的数字集群无线Ad Hoc网络

T. Jurdzinski, D. Kowalski, M. Różański, Grzegorz Stachowiak
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引用次数: 4

摘要

我们考虑了在没有预定义基础结构的SINR模型中具有相同设备的无线自组织网络中的确定性分布式通信。该模型中的大多数算法结果依赖于额外的特征或功能,例如,随机化、地理坐标访问、功率控制、具有各种测量精度的载波传感和干扰消除。我们研究的是一个纯场景,当没有这些特性可用时。针对本文所考虑的局部和全局广播问题,近年来已经提出了几种分布式算法。然而,所有这些解决方案要么是随机的,要么依赖于网络节点在给定度量空间中知道自己的坐标的假设,或者设备的信号灵敏度限制在某个区域(通常小于传输范围)。相比之下,本文的目的是检查在没有随机化、位置可用性、有限灵敏度、功率控制、载波传感、干扰消除或其他特征的情况下,解决方案的效率如何。我们的研究目标有双重动机。首先,检验随机化的必要性和影响是算法设计中一个自然的研究课题。此外,由于无线自组织网络通常是由由电池运行的计算有限的设备构建的,因此希望使用简单且节能的算法,这些算法不需要访问多个传感功能或真正的随机性。作为一种通用工具,我们开发了一种确定性分布式聚类算法,该算法将多跳自组织网络的节点划分为恒定直径的聚类。我们的解决方案依赖于一种新的组合结构(称为目击强选择器),这可能是独立的兴趣。使用聚类,我们开发了一种确定性分布式本地广播算法,在O(Δ log N log N)轮中完成该任务,其中Δ是网络的密度。这是纯场景中的第一个解决方案,距离普遍下界Ω(Δ)只有polylog(n),对于随机化和其他特征的场景也有效。因此,我们得出结论,这些特征对本地广播任务都没有实质性的帮助。使用聚类,我们还构建了一个确定性的全局广播算法,该算法在O(D) (Δ + log?N (log N)轮,其中D是网络的直径。该结果由一个下界Ω(DΔ1-1/∝)补充,其中∝> 2为环境的路径损失参数。鉴于以前的工作,这个下界表明,随机化或自己位置的知识在全局广播中有很大帮助(通过Δ中的因子多项式)。类似的基于聚类的技术可以用于构建唤醒问题和全局领导者选举问题的有效解决方案(与下限相比)。综上所述,我们的研究结果证明,额外的模型/环境特征可能有助于为全球通信问题设计高效的解决方案,但在局部问题的情况下作用不大。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Deterministic Digital Clustering of Wireless Ad Hoc Networks
We consider deterministic distributed communication in wireless ad hoc networks of identical devices in the SINR model without predefined infrastructure. Most algorithmic results in this model rely on additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and interference cancellation. We study a pure scenario, when no such features are available. Several distributed algorithms have been presented in recent years for the local and global broadcast problems considered in this paper. However, all these solutions were either randomized or relied on the assumption that nodes of a network know their own coordinates in a given metric space or devices has signal sensitivity limited to some area (typically smaller than transmission range). In contrast, the aim of this paper is to check how efficient could be solutions without randomization, availability of locations, limited sensitivity, power control, carrier sensing, interference cancellation or other features. Our research objective is motivated twofolds. Firstly, examination of necessity and impacf of randomization is a natural research topic in algorithm design. Moreover, as wireless ad hoc networks are usually built from computationally limited devices run on batteries, it is desirable to use simple and energy efficient algorithms which do not need access to several sensing capabilities or true randomness. As a general tool, we develop a deterministic distributed clustering algorithm, which splits nodes of a multi-hop ad hoc network into clusters of constant diameter. Our solution relies on a new type of combinatorial structures (called witnessed strong selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in O(Δ log N log N) rounds, where Δ is the density of a network. This is the first solution in pure scenario which is only polylog(n) away from the universal lower bound Ω(Δ), valid also for scenarios with randomization and other features. Therefore, we conclude that none of these features substantially helps for the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within O(D(Δ + log? N) log N) rounds, where D is the diameter of the network. This result is complemented by a lower bound Ω(DΔ1-1/∝ ), where ∝ > 2 is the path-loss parameter of the environment. This lower bound, in view of previous work, shows that randomization or knowledge of own location help substantially (by a factor polynomial in Δ) in the global broadcast. Similar clusterbased techniques can be used to build efficient (comparing to the lower bound) solutions to the wake-up problem and the global leader election problem. Summarizing, our results prove that additional model/environment features may help substantially in design of time-efficient solutions for global communication problems, but not much in case of local problems.
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