Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures) and controlled by an adversary. In the first model, the processes transitively communicate their ids in synchronous rounds along a rooted tree given in each round by the adversary whose goal is to maximize the number of rounds until at least one id is known by all processes. Previous research has shown a $\lceil{\frac{3n-1}{2}}\rceil-2$ lower bound and an $O(n\log\log n)$ upper bound. We show the first linear upper bound for this problem, namely $\lceil{(1 + \sqrt 2) n-1}\rceil \approx 2.4n$. We extend these results to the setting where the adversary gives in each round $k$-disjoint forests and their goal is to maximize the number of rounds until there is a set of $k$ ids such that each process knows of at least one of them. We give a $\left\lceil{\frac{3(n-k)}{2}}\right\rceil-1$ lower bound and a $\frac{\pi^2+6}{6}n+1 \approx 2.6n$ upper bound for this problem. Finally, we study the setting where the adversary gives in each round a directed graph with $k$ roots and their goal is to maximize the number of rounds until there exist $k$ ids that are known by all processes. We give a $\left\lceil{\frac{3(n-3k)}{2}}\right\rceil+2$ lower bound and a $\lceil { (1+\sqrt{2})n}\rceil+k-1 \approx 2.4n+k$ upper bound for this problem. For the two latter problems no upper or lower bounds were previously known.

翻译：数据传播是分布式计算中的基本任务。本文研究了多种创新模型中的广播问题，这些模型中连接$n$个进程的通信网络是动态的（例如，由于移动性或故障）并由对手控制。在第一个模型中，进程在同步轮次中沿着对手每轮给出的有根树传递性地通信各自的标识符，对手的目标是最大化至少一个标识符被所有进程知晓所需的轮次数。先前研究给出了$\lceil{\frac{3n-1}{2}}\rceil-2$的下界和$O(n\log\log n)$的上界。我们展示了该问题的首个线性上界，即$\lceil{(1 + \sqrt 2) n-1}\rceil \approx 2.4n$。我们将这些结果推广到对手每轮给出$k$个不相交森林的场景，其目标是最大化存在一组$k$个标识符使得每个进程至少知晓其中一个所需的轮次数。我们对该问题给出了$\left\lceil{\frac{3(n-k)}{2}}\right\rceil-1$的下界和$\frac{\pi^2+6}{6}n+1 \approx 2.6n$的上界。最后，我们研究了对手每轮给出一个具有$k$个根的有向图的场景，其目标是最大化存在$k$个被所有进程知晓的标识符所需的轮次数。我们对该问题给出了$\left\lceil{\frac{3(n-3k)}{2}}\right\rceil+2$的下界和$\lceil { (1+\sqrt{2})n}\rceil+k-1 \approx 2.4n+k$的上界。对于后两个问题，此前尚无已知的上界或下界。