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 the MLDA problem that consists of up to n - 1 aggregation trees and achieves lifetime T o , 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 = ( T o - n + 1 ) / T o . Since in practice T o ≫ 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.