The Kuhn-Munkres Algorithm, also known as the Hungarian Algorithm, is an efficient method for finding the optimal assignment in a weighted bipartite graph, minimizing the total cost. It is widely used in operations research and computer science for solving assignment problems, such as matching tasks to workers in a cost-effective manner.

Kuhn-Munkres Algorithm

The Hungarian Algorithm is an efficient combinatorial optimization algorithm that solves the assignment problem in polynomial time by finding the optimal matching in a weighted bipartite graph. It guarantees finding the minimum cost perfect matching, making it highly useful in applications like job assignment and resource allocation.

Hungarian Algorithm

optimal assignment

A weighted bipartite graph is a type of graph that is divided into two distinct sets of vertices with edges connecting only between these sets, not within them, and each edge has an associated weight. This structure is particularly useful for modeling and solving problems where relationships between two different types of entities need to be quantified, such as in assignment problems, matching problems, or network flow problems.

weighted bipartite graph

minimizing the total cost

Operations research is a discipline that applies advanced analytical methods to help make better decisions by optimizing complex systems. It integrates techniques from mathematics, statistics, and computer science to solve problems in various domains such as logistics, manufacturing, and finance.

operations research

Computer science is the study of algorithmic processes, computational machines, and computation itself, which underpins the development of software and systems that drive modern technology. It encompasses a wide range of topics from theoretical foundations to practical applications, making it essential for innovation in various fields such as artificial intelligence, cybersecurity, and data science.

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