Tight bounds for delay-sensitive aggregation
Yvonne Anne Oswald, Stefan Schmid, Roger P. Wattenhofer · 2008
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 an 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)).