Fully-adaptive Model for Broadcasting with Universal Lists

In classical broadcasting, a piece of information must be transmitted to all entities of a network as quickly as possible, starting from a particular member. Since this problem has an enormous number of applications and is proven to be NP-Hard, several models are defined in the literature while trying to simulate real-world situations and relax several constraints. A well-known branch of broadcasting utilizes a universal list throughout the process. That is, once a vertex is informed, it must follow its corresponding list, regardless of the originator and the neighbor it received the message. The problem of broadcasting with universal lists could be categorized into two sub-models: non-adaptive and adaptive. In the latter model, a sender will skip the vertices on its list from which it has received the message, while those vertices will not be skipped in the first model.In this study, we will present another sub-model called fully adaptive. Not only does this model benefit from a significantly better space complexity compared to the classical model, but, as will be proved, it is faster than the two other sub-models. Since the suggested model fits real-world network architectures, we will design optimal broadcast algorithms for well-known interconnection networks such as trees, grids, and cube-connected cycles under the fully-adaptive model. We also present a tight upper bound for tori under the same model.