Tight bounds for delay-sensitive aggregation

Abstract

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 Ω(min(h, c)). For chain networks, we prove a tight competitive ratio of Θ(min ( √ h, c)). Furthermore, the paper introduces a new model for online event aggregation where the importance of an event depends on its difference to previous events.

Latency Constrained Aggregation in Chain Networks Admits a PTAS

“…Therefore, by combining Inequalities (16) and (17) with Inequality (14), we conclude that, for each level i ≤ i ′ ,…”

“…A closely related problem is the Multicast Acknowledgement Problem [4,11,16], where we also want to aggregate messages in a tree topology, but we do not have fixed deadlines. Instead, the objective is to minimize the total sending costs plus the sum of delays, which is closely related to the well-known flow time objective from scheduling.…”

When In-Network Processing Meets Time: Complexity and Effects of Joint Optimization in Wireless Sensor Networks

“…Not focusing on mission-critical sensornets, however, these works have mostly ignored the timeliness of data delivery when designing INP mechanisms. Recently, Becchetti et al [3] and Oswald et al [4] examined the issue of data delivery latency in in-network processing. Theoretical in nature, these studies assumed total aggregation where any arbitrary number of information elements (e.g., reports after an event detection) can be aggregated into one single packet, which may well be infeasible in many practical settings.…”

“…Unlike total aggregation assumed in [3] and [4], the number of information elements that can be aggregated into a single packet is constrained by the maximum packet size, thus we have to carefully schedule information element transmissions so that the degree of packet packing (i.e., the amount of sensing data contained in packets) can be maximized without violating application requirement on the timeliness of data delivery. As a first step toward understanding the complexity of jointly optimizing INP and QoS with aggregation constraints, we analyze the impact that aggregation constraints have on the computational complexity of the problem, and we prove the following:…”

“…transmission time from any leaf node to its parent t 2 transmission time from any node v j to node v t 3 transmission time from node v to node s t 4 transmission time from any node v c i to node v the system model and precisely define the joint optimization problem in Section II. Then we analyze the complexity of the problem in Section III, and present the tPack protocol in Section IV.…”