Embedding data-aggregation capabilities into sensor nodes of wireless networks could save energy by reducing redundant data flow transmissions. Existing research describes the construction of data aggregation trees to maximize data aggregation times in order to reduce data transmission of redundant data. However, aggregation of more nodes on the same node will incur significant collisions. These MAC (Media Access Control) layer collisions introduce additional data retransmissions that could jeopardize the advantages of data aggregation. This paper is the first to consider the energy consumption tradeoffs between data aggregation and retransmissions in a wireless sensor network. By using the existing CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance) MAC protocol, the retransmission energy consumption function is well formulated. This paper proposes a novel non-linear mathematical formulation, whose function is to minimize the total energy consumption of data transmission subject to data aggregation trees and data retransmissions. This solution approach is based on Lagrangean relaxation, in conjunction with optimization-based heuristics. From the computational experiments, it is shown that the proposed algorithms could construct MAC aware data aggregation trees that are up to 59% more energy efficient than existing data aggregation algorithms.
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