Optimal energy-balanced algorithm for selection in a single hop sensor network

Sensor networks are being used to implement a large set of applications that require distributed, collaborative computations. Selection is an important kernel in several sensor applications, particularly those involving speech and image data processing. In this paper we present an energy and time optimal algorithm for the selection problem in a single hop wireless network. The algorithm also has the property that it is energy-balanced. This implies that all sensors dissipate asymptotically equal amount of energy. Uniform energy dissipation is desirable as it enables the network to remain fully functional for the maximum time. We demonstrate that in a single hop, single channel network of n randomly distributed sensors, selection can be performed in O(n) time and O(n) energy, with no sensor being awake for more than O(1) time steps. We extend our results for a p-channel network, where p≤n^1-ε and 0<ε≤1. We show that selection can be performed in time O(n/p) and energy O(n) with no sensor being awake for more than O(1) time steps.