Combinatorial optimization is a subset of mathematical optimization that is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, mathematics, auction theory, and software engineering. Combinatorial optimization is a lively field of applied mathematics combining techniques from combinatorics linear programming and the theory of algorithms to solve optimization problems over discrete structures. This book provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization.

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