Competitive Analysis of Organization Networks or Multicast Acknowledgment: How Much to Wait?

We study, from the perspective of competitive analysis, the trade‐off between communication cost and delay cost, or simply the send‐or‐wait dilemma on a hierarchical rooted tree. The problem is an abstraction of the message aggregation problem on communication networks and an organizational problem in network hierarchies. We consider the most natural variant of the problem, the distributed asynchronous regime, and give tight (within a small additive constant) upper and lower bounds on the competitive ratio of the optimization problem. We also consider the centralized version of the problem, in which there is a central entity which remains updated about any incoming messages to the network and which can control the internal delivery of messages in the network. For the centralized setting, we combine a natural rent‐to‐buy strategy with prediction techniques to achieve the first constant competitive ratio algorithm for any non‐trivial class of network topologies.