A combinatorial algorithm for the maximum lifetime data gathering with aggregation problem in sensor networks

Performing tasks energy efficiently in a wireless sensor network (WSN) is a critical issue for the successful deployment and operation of such networks. Gathering data from all the sensors to a base station, especially with in–network aggregation, is an important problem that has received a lot of attention recently. The Maximum Lifetime Data Gathering with Aggregation (MLDA) problem deals 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. A solution of value T to the MLDA problem consists of a collection of aggregation trees together with the number of rounds each such tree should be used in order to achieve lifetime T . We describe a combinatorial iterative algorithm for finding an optimal continuous solution to theMLDA problem that consists of up to n−1 aggregation trees and achieves lifetime To, which depends on the network topology and initial energy available at the sensors. We obtain an α–approximate optimal integral solution by simply rounding down the optimal continuous solution, where α = (To−n+1)/To. Since in practice To n, α ≈ 1. We get asymptotically optimal integral solutions to the MLDA problem whenever the optimal continuous solution is ω(n). Furthermore, we demonstrate the efficiency and effectiveness of the proposed algorithm via extensive experimental results.