We study here 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 to carry out a given task. Also, the distributed task itself may now require a global reconfiguration from a given initial network \(G_s\) to a target network \(G_f\) from a desirable family of networks. To formally capture costs associated with creating and maintaining connections, we define three edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. We give (poly)log(n) time algorithms for the task of transforming any \(G_s\) into a \(G_f\) of diameter (poly)log(n), while minimizing the edge-complexity. Our main lower bound shows that \(\varOmega (n)\) total edge activations and \(\varOmega (n/\log n)\) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of \(\varTheta (\log n)\) rounds. We give three distributed algorithms for our general task. The first runs in \(O(\log n)\) time, with at most 2n active edges per round, a 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. It gives a target network of diameter \(O(\log n)\) and uses O(n) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve \(o(\log ^2 n)\) running time.

我们在这里研究可以主动修改其通信网络的分布式实体系统。这产生了分布式算法，除了通信之外，这些算法还可以利用网络重新配置来执行给定的任务。此外，分布式任务本身现在可能需要从给定的初始网络\(G_s\)到来自理想网络系列的目标网络\(G_f\)的全局重新配置。为了正式捕获与创建和维护连接相关的成本，我们定义了三个边复杂度度量：总边激活、每轮最大激活边和节点的最大激活度。我们给 (poly)log( n) 将任何\(G_s\)转换为直径 (poly)log( n )的\(G_f\)任务的时间算法，同时最小化边缘复杂度。我们的主要下界表明\(\varOmega (n)\)总边缘激活和\(\varOmega (n/\log n)\)每轮激活必须由任何算法（即使是集中式）实现最佳\(\varTheta (\log n)\)轮。我们为我们的一般任务提供了三种分布式算法。第一次在\(O(\log n)\)时间内运行，每轮最多有 2 n 个活动边，总共\(O(n\log n)\) 个边激活，最大程度\(n- 1\)，以及直径为 2 的目标网络。第二个通过在时间和总边缘激活中支付额外的对数因子来实现有界度。它给出了一个直径为\(O(\log n)\)的目标网络，并且每轮使用O ( n ) 个活动边。我们的第三个算法表明，如果我们稍微增加 polylog( n )的最大度数，那么我们可以达到\(o(\log ^2 n)\)运行时间。