Graph-Based Geographic Region Optimization for Contiguous Resource Allocation

The patent segments the geographic optimization problem into two distinct components: a master problem that handles resource allocation and area assignment, and a subproblem that verifies contiguity constraints and generates additional feasible solutions. This segmentation transforms the intractable single mixed integer programming problem into a more manageable column generation framework, where the master problem remains computationally feasible and the contiguity constraints are enforced through the subproblem's path-finding algorithm.

The patent substitutes the traditional flow-based mechanical system with a graph-based computational system. Instead of using flow networks to model resource allocation and geographic assignment, the patent employs graph theory concepts including nodes representing geographic areas, edges representing adjacency relationships, and path-finding algorithms to enforce contiguity. This substitution leverages efficient graph algorithms (such as BFS/DFS for contiguity verification and shortest path algorithms for optimization) that are computationally superior to flow-based methods for this specific problem type, achieving at least thirteen times faster solution times.