On enumeration of Spanning Arborescences and Reliability for Network Broadcast in Fixed-Schedule Dynamic Networks

This paper considers broadcast communications or information dissemination in Fixed-Schedule Dynamic Networks (FSDNs). It shows that the notion of spanning arborescences, common used in static networks, is not acceptable in FSDNs. This paper then introduces two new concepts on spanning arborescences: (i) t-arborescence -- an arborescence in which all edges have contact schedules, and (ii) tv-arborescence -- a t arborescence that requires time-ordered edges. The paper discusses properties of these spanning arborscences, and proposes two novel methods, TA-to-TVA and A-to-TVA, that utilize Tutte's Matrix-Tree theorem to enumerate all tv-arborscences. 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 tv-arborescences to compute these reliability metrics. Our simulations with ten arbitrary FSDNs show that A-to-TVA, which generates tv-arborescences from static arborescences, is more time efficient than TA-to-TVA, which enumerates them from t-arborescences. Besides, it is found that nodes having more tv-arborescneces do not always yield a higher broadcast reliability.