A Strict Hierarchy of Dynamic Graphs for Shortest, Fastest, and Foremost Broadcast

The notion ofhighly dynamic networks encompasses many real-world contexts. The need to categori z and understand them led the engineering community to design a va riety of mobility models , based on which experiments can be reproduced and solutions fairly compared. The theoretical analogues of mobility models are the logical properties of the network dynamics that allow the ta xonomy of various of classes of dynamic graphs. In this paper we study the relationship between three classes o f (highly) dynamic networks by means of studying the feasibility of several variants of the broadcast, namel y shortest , fastest , andforemostbroadcast. We focus on those graphs in which re-appearance of the edges is either recurrent(classR), bounded-recurrent (B), or periodic(P), together with the knowledge of n (the number of nodes), ∆ (a bound on the recurrence time), or p (the period). By studying the feasibility of shortest, fast est, and foremost broadcasts within these classes, we show their computational power forms a strict hierarchy. In fact, we show that P(Rn) ( P(B∆) ( P(Pp), whereP(Ck) is the set of problems one can solve in class C with knowledgek. Interestingly, we also find that all three variants of the broadcast have distinct features r elative to feasibility (and to a lesser extent complexity), which suggests some order of difficulty among them. Two disti nct orders can actually be proposed depending on whether the parameter of interest is the mere f asibilityor also involves thereusabilityof a solution (i.e., in this paper, the broadcast tree).