This paper considers broadcast communications or information dissemination in Fixed-Schedule Dynamic Networks (FSDNs). It shows that the notion of spanning arborescences, commonly used in static networks, is not applicable in FSDNs. This paper then introduces two new concepts on spanning arborescences: (i) ${\boldsymbol{t}}$ -arborescence – an arborescence in which all edges have contact schedules, and (ii) ${\boldsymbol{tv}}$ -arborescence – a ${\boldsymbol{t}}$ -arborescence that requires time-ordered edges to establish a communication scenario. The paper discusses properties of these spanning arborescences, and proposes two novel methods, TA-to-TVA and A-to-TVA, that utilize Tutte's Matrix-Tree theorem to enumerate all ${\boldsymbol{tv}}$ -arborescences. Next, it considers edges in FSDNs with a probability of failure, and proposes two new broadcast reliability metrics. Then, this paper shows how to use ${\boldsymbol{tv}}$ -arborescences to compute these reliability metrics. Our simulations with ten arbitrary FSDNs show that A-to-TVA, which generates ${\boldsymbol{tv}}$ -arborescences from static arborescences, is more time efficient than TA-to-TVA, which enumerates them from ${\boldsymbol{t}}$ -arborescences. They also show that nodes having more ${\boldsymbol{tv}}$ -arborescences do not always yield a higher broadcast reliability.

中文翻译：

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固定调度动态网络中生成树的枚举与网络广播的可靠性

本文考虑固定时间表动态网络（FSDN）中的广播通信或信息传播。它显示了跨树状的概念，通常用于静态的网络，不适用于FSDN。然后，本文介绍了有关跨越树状结构的两个新概念：（i）$ {\ boldsymbol {t}} $ -树木状–所有边缘都有接触时间表的树木状，并且（ii） $ {\ boldsymbol {tv}} $ -树状– $ {\ boldsymbol {t}} $ -树状结构，需要按时间顺序排列的边缘来建立通信场景。本文讨论了这些跨越树状结构的性质，并提出了两种新颖的方法，即TA-to-TVA和A-to-TVA，它们利用Tutte的矩阵树定理来枚举所有$ {\ boldsymbol {tv}} $ -树状。接下来，它考虑了具有故障可能性的FSDN中的边缘，并提出了两个新的广播可靠性指标。然后，本文展示了如何使用$ {\ boldsymbol {tv}} $ -树状计算这些可靠性指标。我们对十个任意FSDN的仿真表明，A-to-TVA可以生成$ {\ boldsymbol {tv}} $ -来自 静态的 树状结构比从TA到TVA的时间效率更高，后者从 $ {\ boldsymbol {t}} $ -树状。他们还表明节点具有更多$ {\ boldsymbol {tv}} $ -树状发光并不总是产生更高的广播可靠性。