Methods for Reducing the Complexity of Critical Functions Computations for Antenna Placement Problems Using Brute Force Algorithm

The optimal placement of antennas in the wireless network design is determined by two key functions: maximizing coverage and minimizing overlap areas. Finding an optimal solution requires the evaluation of all potential placements that can demand significant computational resources, especially as the grid size, network scale, or the number of antennas increases. The brute force approach systematically explores every placement combination, calculating coverage and overlap areas for each placement. However, its computational cost becomes prohibitive for large-scale networks. To address this challenge, we propose various complexity reduction methods: pre-computation of distances and overlap areas between antennas, search space reduction to limit the number of candidate placements, and parallel computing to distribute the workload across multiple processors. We can apply these methods individually or in combination to improve the efficiency of the brute force algorithm for small or large-scale wireless network deployments. Experimental results demonstrate the effectiveness of these methods in significantly reducing computation time. When applied individually, the best method can reduce computation time from over 144 000 to 6.1 s without compromising accuracy. Combining all three strategies yielded the most significant improvement, reducing computation time to just 0.23 s while maintaining accuracy in calculating critical functions. These results highlight the potential of our proposed methodology to improve significantly the scalability and practicality of brute force solutions in wireless network design. Furthermore, the approach broadly applies to other optimization problems where computational complexity is a key constraint, making it a versatile and powerful tool for real-time and large-scale network deployments.