Richard Karp's 1972 paper "Reductability Among Combinatorial Problems" is an important paper in the field of computer science that laid the foundation for computational complexity theory, particularly in understanding the concept of NP completeness. Core idea: The core idea of this paper is to prove that a series of important combinatorial problems have the same computational difficulty, that is, they all belong to NP complete problems. This means that if any of these problems have an efficient solution (which can be solved in polynomial time), then all NP problems will have an efficient solution, i.e. P=NP. However, whether P equals NP is one of the most famous unsolved problems in computer science. Main contributions: Defined the concept of polynomial time reduction: Kapu introduced the concept of polynomial time reduction, which is a method of transforming one problem into another, and the transformation process can be completed in polynomial time. If problem A can be reduced to problem B in polynomial time, then the difficulty of problem A will not exceed that of problem B. Proved that 21 classical problems are NP complete: Kapu proved that 21 classical combinatorial problems, including set cover, vertex cover, Hamiltonian circuit, traveling salesman problem, etc., are NP complete. These problems cover multiple fields such as graph theory, set theory, logic, etc. Their NP completeness indicates the computational difficulty of such problems. Laying the foundation for the theory of NP completeness: Kapu's paper laid the groundwork for the development of NP completeness theory. His research results not only deepen people's understanding of computational complexity, but also provide important tools and methods for subsequent research. importance: Kapu's paper "Reductability in combinatorial problems" is a milestone work in computational complexity theory. It: The importance of establishing the concept of NP completeness: The NP complete problem is one of the most challenging problems in computer science, and understanding NP completeness is of great significance for researching algorithms, artificial intelligence, and other fields. Promoted the development of computational complexity theory: Kapu's work sparked extensive research, and people began to pay attention to the computational complexity of various problems and attempt to find efficient algorithms. The research results on NP complete problems have significant implications for many practical applications, such as cryptography and optimization problems. In summary, Richard Karp's paper "Reductability in combinatorial problems" is a classic work in the field of computer science, which has made outstanding contributions to the development of computational complexity theory and still has significant influence today.