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Tight Bounds for Delay-Sensitive Aggregation
Citation key PSW-TBDSA-10
Author Pignolet, Yvonne Anne and Schmid, Stefan and Wattenhofer, Roger
Pages 39–58
Year 2010
ISSN 1365-8050
Journal Discrete Mathematics and Theoretical Computer Science Journal
Volume 12
Number 1
Month February
Abstract This article studies the fundamental trade-off between delay and communication cost in networks. We consider an online optimization problem where nodes are organized in a tree topology. The nodes seek to minimize the time until the root is informed about the changes of their states and to use as few transmissions as possible. 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 Ω(min(h,c)). For chain networks, we prove a tight competitive ratio of Θ(min(radic(h),c)). Furthermore, we introduce a model for value-sensitive aggregation, where the cost depends on the number of transmissions and the error at the root.
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