Latency Constrained Aggregation in Chain Networks Admits a PTAS

Abstract

This paper studies the aggregation of messages in networks that consist of a chain of nodes, and each message is time-constrained such that it needs to be aggregated during a given time interval, called its due interval. The objective is to minimize the maximum sending cost of any node, which is for example a concern in wireless sensor networks, where it is crucial to distribute the energy consumption as equally as possible. First, we settle the complexity of this problem by proving its NP-hardness, even for the case of unit length due intervals. Second, we give a QPTAS, which we extend to a PTAS for the special case that the lengths of the due intervals are constants. This is in particular interesting, since we prove that this problem becomes APX-hard if we consider tree networks instead of chain networks, even for the case of unit length due intervals. Specifically, we show that it cannot be approximated within 4/3 − ǫ for any ǫ > 0, unless P=NP.

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

“…Most closely related to our work are [3], [27], [28] where the authors studied the issue of optimizing INP under the constraint of end-to-end data delivery latency. But these studies did not consider aggregation constraints and instead assumed total aggregation where any arbitrary number of information elements can be aggregated into one single packet.…”