动态网络中随时可用生成树的分布式维护
Distributed Maintenance of Anytime Available Spanning Trees in Dynamic Networks
摘要：
我们解决的问题，建立和维护分布式生成树在高度动态的网络中，拓扑事件可以发生在任何时间和任何速率，并没有稳定的时期可以假设。在这些恶劣的环境中，我们努力保留一些属性，例如无周期性或每棵树中根的存在，以便能够（在可能的范围内）不间断地使用这些树。我们的算法在一个粗粒度的水平上运行，使用原子的成对相互作用的方式类似于最近的人口协议模型。该算法依赖于生成树森林的\emph{topology-induced splittings}和\emph{computation-induced mergings}的永久交替。林中的每棵树都只托管一个令牌（也称为根），该令牌在树中执行{ \em inside}随机游走，在跨越边时切换父子关系。当两个标记位于同一条边的两侧时，它们的树在该边上合并，并且一个标记消失。每当属于树的边消失时，其子端点立即重新生成一个新标记。这种方法的主要特点是\emph{merging}和\emph{splitting}都是纯粹的局部化现象。在本文中，我们提出和激励的算法，我们证明了它的正确性，在任意动态网络。然后，我们讨论围绕这个一般原则的几个实现选择。关于其分析的初步结果也进行了讨论，特别是在静态上下文中的两个给定的树的预期合并时间的解析表达式。
英文摘要：
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we strive to preserve some properties such as cycle-freeness or the existence of a root in each tree, in order to make it possible to keep using the trees uninterruptedly (to a possible extent). Our algorithm operates at a coarse-grain level, using atomic pairwise interactions in a way akin to recent population protocol models. The algorithm relies on a perpetual alternation of \emph{topology-induced splittings} and \emph{computation-induced mergings} of a forest of spanning trees. Each tree in the forest hosts exactly one token (also called root) that performs a random walk {\em inside} the tree, switching parent-child relationships as it crosses edges. When two tokens are located on both sides of a same edge, their trees are merged upon this edge and one token disappears. Whenever an edge that belongs to a tree disappears, its child endpoint regenerates a new token instantly. The main features of this approach is that both \emph{merging} and \emph{splitting} are purely localized phenomenons. In this paper, we present and motivate the algorithm, and we prove its correctness in arbitrary dynamic networks. Then we discuss several implementation choices around this general principle. Preliminary results regarding its analysis are also discussed, in particular an analytical expression of the expected merging time for two given trees in a static context.
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。
