在本文中，我们研究系统的分布式实体，可以主动修改他们的通信网络。这就产生了分布式算法，除了通信，还可以利用网络重新配置，以执行给定的任务。同时，分布式任务本身现在可能需要从给定的初始网络$G_s$全局重新配置到来自具有一些良好属性（如小直径）的网络族的目标网络$G_f$。有了相当强大的计算实体，有一个简单的算法，将任何$G_s$转换成一个生成集团在$O(\log n)$时间。然后，该算法可以计算输入的任何全局函数，并在一轮中重新配置到任何目标网络。我们认为，这样的策略是不切实际的实际应用。在真实的动态网络中，创建和维护连接是有成本的。为了正式捕获这些成本，我们定义了三个边缘复杂性度量：\emph{total edge activations}、\emph{maximum activated edges per round}和\emph{maximum activated degree of a node}。上面强调的集团形成策略，最大化了所有这些。我们的目标是改进算法，实现（聚）日志$(n)$的时间，同时最大限度地减少边缘复杂性的一般任务的任何$G_s$转换成一个$G_f$的直径（聚）日志$(n)$。我们给出了三个分布式算法。第一个在$O(\log n)$时间内运行，每轮最多有$2n$活动边，$O(n\log n)$边激活的最佳总数，最大度$n-1$，以及直径为2的目标网络。第二种方法通过在时间和总边激活数上增加一个对数因子来实现有界度，并给出直径为$O(\log n)$的目标网络。我们的第三个算法表明，如果我们稍微增加polylog $(n)$的最大程度，那么我们可以实现$o(\log^2 n)$的运行时间。
英文摘要：
In this paper, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require global reconfiguration from a given initial network $G_s$ to a target network $G_f$ from a family of networks having some good properties, like small diameter. With reasonably powerful computational entities, there is a straightforward algorithm that transforms any $G_s$ into a spanning clique in $O(\log n)$ time. The algorithm can then compute any global function on inputs and reconfigure to any target network in one round. We argue that such a strategy is impractical for real applications. In real dynamic networks there is a cost associated with creating and maintaining connections. To formally capture such costs, we define three edge-complexity measures: the \emph{total edge activations}, the \emph{maximum activated edges per round}, and the \emph{maximum activated degree of a node}. The clique formation strategy highlighted above, maximizes all of them. We aim at improved algorithms that achieve (poly)log$(n)$ time while minimizing the edge-complexity for the general task of transforming any $G_s$ into a $G_f$ of diameter (poly)log$(n)$. We give three distributed algorithms. The first runs in $O(\log n)$ time, with at most $2n$ active edges per round, an optimal total of $O(n\log n)$ edge activations, a maximum degree $n-1$, and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations and gives a target network of diameter $O(\log n)$. Our third algorithm shows that if we slightly increase the maximum degree to polylog$(n)$ then we can achieve a running time of $o(\log^2 n)$.
Enabling Reconfiguration-Communication Overlap for Collective Communication in Optical Networks
School of Computer Science and Technology, University of Science and Technology of China (USTC)（科学技术大学计算机科学与技术学院）；Shanghai Innovation Institute（上海创新研究院）；Suzhou Institute for Advanced Research, USTC（先进研究院，USTC）
