TIGHT ANALYSIS OF SHORTEST PATH CONVERGECAST IN WIRELESS SENSOR NETWORKS
We consider the convergecast problem in wireless sensor networks where each sensor has a reading that must reach a designated sink. Since a sensor reading can usually be encoded in a few bytes, more than one reading can readily fit into a standard transmission packet. We assume that each packet hop consumes one unit of energy. Our objective is to minimize the total energy consumed to send all readings to the sink. We show that this problem is NP-hard even when all readings are of fixed size. We then study a class SPEP of distributed algorithms that is completely defined by two properties. Firstly, the packets hop along some shortest path to the sink. Secondly, the nodes use an elementary packing algorithm to pack readings into packets. Our main technical contribution is a lower bound. We show that no algorithm for UCCP that either follows the shortest path or packs in an elementary manner is a (2 − ϵ)-approximation, for any fixed ϵ > 0. To complement this, we show that SPEP algorithms are [Formula: see text]-approximation for UCCP and 3-approximation for CCP, where k ≥ 2 is the number of readings that can fit within a packet. We conclude with some special cases and experimental observations.