A Branch-and-Cut Approach for the Minimum-Energy Broadcasting Problem in Wireless Networks

This paper studies the minimum-energy broadcasting problem (MEBP) in wireless sensor networks. The aim of the MEBP is to determine the power assignment of each node in a wireless sensor network such that a specified source node can broadcast messages to each of the other nodes and the total energy consumption is minimized. We first present a new formulation involving an exponential number of constraints for the broadcasting requirement. We then prove that under a mild condition, these constraints for the broadcasting requirement are facet defining. Directly using the proposed formulation, we further present a new branch-and-cut (B&C) solution approach to optimally solve the MEBP. We propose three ways to identify violated cuts at each node in the enumeration tree. Finally, we test the proposed B&C approach on 1,000 randomly generated instances with different properties and compare it with other alternative methods in the literature. Computational results demonstrate the effectiveness and efficiency of our approach using the proposed formulation for instances with up to 100 nodes.