Energy-optimal and energy-balanced sorting in a single-hop wireless sensor network

A large number of sensors networked together form selforganizing pervasive systems that provide the basis for implementation of several applications involving distributed, collaborative computations. Energy dissipation is a critical issue for these networks, as their life-time is limited by the battery power of the sensors. In this paper, we focus on design of an energy-balanced, energy-optimal algorithm for sorting in a single-hop sensor network. Energy optimality implies that the overall energy dissipation in the system is minimized. Energy-balancedness ensures that all the sensors spend asymptotically equivalent amount of energy in the system. Uniform energy dissipation is desirable as it enables the network to remain fully functional for the maximum time. We demonstrate that given a single-hop, singlechannel network of n randomly distributed sensors, sorting can be performed in O(n log n) time and energy, with no sensor being awake for more than O(log n) time steps. In a p-channel network, where p ∓ n^1-ϵ for 0 < ϵ ∓ 1, sorting can be performed in O(n = p log n) time and O(n log n) energy with no node being awake for more than O(log n) time steps.