GP Algorithm (Gomory-Hu Tree Implementation)

In the field of computer science, the GP algorithm (commonly known as the Gomory-Hu Tree algorithm) serves as a widely adopted method for solving graph cut problems. This algorithm primarily addresses minimum cut computations by first constructing a Gomory-Hu tree - a compact data structure that encapsulates all pairwise minimum cuts in a weighted undirected graph. The implementation typically involves recursive partitioning where each step selects a vertex pair, computes their minimum cut using max-flow algorithms like Ford-Fulkerson or Push-Relabel, and contracts the graph accordingly. Through recursive tree traversals, the algorithm efficiently derives all cut values while maintaining O(n) storage complexity for n vertices. Owing to its O(n) flow computations and robust accuracy, the GP algorithm has gained prominence in applications such as graph partitioning, clustering algorithms, and community detection systems, where it often serves as a foundational component for network analysis pipelines.