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Combinatorial optimization is a subfield 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 , software engineering , 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. Typical problems are the travelling salesman problem "TSP" , the minimum spanning tree problem "MST" , and the knapsack problem.
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Discrete or combinatorial optimization embodies a vast and significant area of combinatorics that interfaces many related subjects. Included among these are linear programming, operations research, theory of algorithms and computational complexity. Much of combinatorial optimization is motivated by very simple and natural problems such as routing problems in networks, packing and covering problems in graph theory, scheduling problems, and sorting problems. But the methodology of the subject encompasses a variety of techniques ranging from elementary tree-growing procedures to constructions of Hilbert bases of integer lattices. The growth of this area has been linked with the development of linear programming and of graph theory over the last forty years.
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Part of the Algorithms and Combinatorics book series AC, volume It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics paths, flows, matching, matroids, NP-completeness, approximation algorithms in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Thus, this book represents the state of the art of combinatorial optimization. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization. It offers a good number of exercises …. This book excels at providing very up-to-date results that give an idea of the state of the art, but also makes it clear that this is still a very active area of research.
Combinatorial Optimization pp Cite as. Many combinatorial optimization problems can be formulated as follows. In the following we consider modular functions c , i. Unable to display preview.
Combinatorial. Optimization: Networks and Matroids. EUGENE L. LAWLER. University Combinatorial optimization problems arise everywhere, and certainly in.
ReplyCombinatorial Optimisation: Networks and Matroids by Eugene Lawler examines shortest paths, network flows, bipartite matching, non bipartite matching. More.
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