Combinatorial optimization:Algorithms and complexity - IEEE Journals & MagazineIn operations research , applied mathematics and theoretical computer science , combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. It operates on the domain of those optimization problems in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution. Some common problems involving combinatorial optimization are the travelling salesman problem "TSP" , the minimum spanning tree problem "MST" , and the knapsack problem. 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 , auction theory , and software engineering. Some research literature  considers discrete optimization to consist of integer programming together with combinatorial optimization which in turn is composed of optimization problems dealing with graph structures although all of these topics have closely intertwined research literature.
Papadimitriou C.H., Steiglitz K. Combinatorial Optimization. Algorithms and Complexity
Springer, Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers.
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