Everywhere sparse approximately optimal minimum energy data gathering and aggregation in sensor networks

Abstract

We consider two related data gathering problems for wireless sensor networks (WSNs). The MLDA problem is concerned with maximizing the system lifetime T so that we can perform T rounds of data gathering with in-network aggregation, given the initial available energy of the sensors. The M 2 EDA problem is concerned with minimizing the maximum energy consumed by any one sensor when performing T rounds of data gathering with in-network aggregation, for a given T . We provide an effective algorithm for finding an everywhere sparse integral solution to the M 2 EDA problem which is within a factor of α = 1+ 4 n / T of the optimum, where n is the number of nodes. A solution is everywhere sparse if the number of communication links for any subset X of nodes is O ( X ), in our case at most 4| X |. Since often T = ω( n ), we obtain the first everywhere sparse, asymptotically optimal integral solutions to the M 2 EDA problem. Everywhere sparse solutions are desirable since then almost all sensors have small number of incident communication links and small overhead for maintaining state. We also show that the MLDA and M 2 EDA problems are essentially equivalent, in the sense that we can obtain an optimal fractional solution to an instance of the MLDA problem by scaling an optimal fractional solution to a suitable instance of the M 2 EDA problem. As a result, our algorithm is effective at finding everywhere sparse, asymptotically optimal, integral solutions to the MLDA problem, when the initial available energy of the sensors is sufficient for supporting optimal system lifetime which is ω( n ).