无线电网络下限变得简单
Radio Network Lower Bounds Made Easy
摘要：
近三十年来，理论界一直在研究无线网络模型中的分布式算法。这项工作的一个重要部分集中在基本的通信问题，如唤醒（一组未知的节点之间的对称性破坏）和广播（通过一个未知的网络拓扑结构的消息传播）的下限。在本文中，我们介绍了一种新的技术证明这种类型的界限，减少从概率击中游戏的基础上，简化和加强了现有的工作。更详细地说，在这篇论文中，我们证明了新的预期时间和高概率下限唤醒和全球广播的无线电网络模型的单和多通道版本，有和没有冲突检测。在这样做的过程中，我们能够重现以前在二十五年内发表的六篇论文的结果。除了简化这些现有的结果，我们的技术，在许多地方，也提高了最先进的：我们证明的八个界限，四个严格加强了最知名的以前的结果（在时间复杂度和/或算法类的一般性，它持有），和三个提供了第一个已知的非平凡的情况下的限制。事实上，同样的技术可以很容易地产生这种不同的集合的下限表明一个令人惊讶的统一基础的通信任务在无线电网络模型-揭示了在内心深处，下面的问题定义和模型假设的细节，在这种设置中的通信减少到找到一个简单的游戏有效的策略。
英文摘要：
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among an unknown set of nodes) and broadcast (message dissemination through an unknown network topology). In this paper, we introduce a new technique for proving this type of bound, based on reduction from a probabilistic hitting game, that simplifies and strengthens much of this existing work. In more detail, in this single paper we prove new expected time and high probability lower bounds for wake-up and global broadcast in single and multichannel versions of the radio network model both with and without collision detection. In doing so, we are able to reproduce results that previously spanned a half-dozen papers published over a period of twenty-five years. In addition to simplifying these existing results, our technique, in many places, also improves the state of the art: of the eight bounds we prove, four strictly strengthen the best known previous result (in terms of time complexity and/or generality of the algorithm class for which it holds), and three provide the first known non-trivial bound for the case in question. The fact that the same technique can easily generate this diverse collection of lower bounds indicates a surprising unity underlying communication tasks in the radio network model---revealing that deep down, below the specifics of the problem definition and model assumptions, communication in this setting reduces to finding efficient strategies for a simple game.
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。
