Tight Bounds for Delay-Sensitive Aggregation

This paper studies the fundamental trade-off between communication cost and delay cost arising in Various contexts such as control message aggregation or organization theory. An optimization problem is considered where nodes are organized in a tree topology. The nodes seek to minimize the time until the root is informed about their states and to use as few transmissions as possible at the same time. We derive all upper bound on the competitive ratio of O(min(h, c)) where h is the tree's height, and c is the transmission cost per edge. Moreover, we prove that this upper bound is tight in the sense that any oblivious algorithm has a ratio of at least Omega(min(h, c)). For chain networks, we prove a tight competitive ratio of Theta(min(root h, c)). Furthermore, the paper introduces a new model for online event aggregation where the importance of ail event depends oil its difference to previous events.