Population Reach Estimation via Tree Graph Association

The patent segments the complex calculation of population reach across unions by breaking it down into individual marginal rating calculations. Instead of computing the entire union directly, it calculates reach for each marginal rating separately and then combines these segmented results using set theory principles, thereby reducing memory and processing requirements while maintaining measurement precision.

The patent introduces an intermediary mathematical framework using Lagrange multipliers and system of equations as a mediator between the raw marginal rating data and the final population reach estimation. This intermediary approach transforms the complex union calculation into a series of manageable linear equations that can be solved iteratively, reducing computational complexity while preserving accuracy.

The patent performs preliminary action by pre-calculating and storing the marginal rating reaches before combining them into union reaches. By preparing the individual marginal components in advance and organizing them into a structured system of equations, the patent reduces the computational burden during the final union calculation phase, thereby decreasing processing time while maintaining accuracy.

The patent employs dynamic programming principles by solving the system of equations iteratively using Lagrange multipliers. Rather than using static numerical methods that process all unions simultaneously, the patent dynamically adjusts the solution through iterative refinement, converging to the accurate reach estimation more efficiently and reducing overall processing time.