Bipartite Matching Algorithms — Hopcroft-Karp, Gale-Shapley & Hungarian Method | Chapter 25 in Introduction to Algorithms
Bipartite Matching Algorithms — Hopcroft-Karp, Gale-Shapley & Hungarian Method | Chapter 25 in Introduction to Algorithms Chapter 25 of Introduction to Algorithms (CLRS) presents a rich collection of algorithms for solving matching problems in bipartite graphs. These problems involve pairing elements from two disjoint sets—such as jobs and workers or students and schools—based on constraints like maximum size, stability, or optimal assignment weights. This chapter explores the powerful Hopcroft-Karp algorithm for maximum matching, the Gale-Shapley algorithm for stable marriage problems, and the Hungarian algorithm for solving the assignment problem with weights. 📺 Watch the full podcast-style summary above, or continue reading for a complete breakdown of the key matching strategies, theorems, and complexity results introduced in Chapter 25. Maximum Bipartite Matching A matching is a set of edges with no shared vertices. In bipartite graphs, the goal is often to fin...