# Graph theory and combinatorial optimization

Graph theory and combinatorial optimization Master Degree

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• Application Deadline:2018/06/12
• Tuition:￥0.00
• Application Fee:￥800.00
• Service Fee:￥0.00
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Combinatorial optimization, also known as combinatorial planning, is a type of mathematical plan that finds an optimal subset of a finite set of all subsets with certain characteristics. At the beginning, the issues it studied, such as the design of broadcasting networks, the arrangement of tourist routes, and the formulation of curriculum, were all extreme questions on the Internet. Later, these problems were summarized and abstracted. In theory, some more general combinatorial optimization problems and algorithms were studied. The main research contents are: linear combination optimization problems; network optimization problems; independent systems and matroids; matroids are a basic and important concept in combinatorial optimization. Many combinatorial problems can be transformed into matroid problems. The greedy algorithm is a simple algorithm to find the optimal independent set of matroids; the interlaced chain algorithm is the basic algorithm to solve the optimal intersection problem. The classification of problem algorithms is also a major research topic. Some algorithms have polynomial time complexity, such as greedy algorithm, interlaced chain algorithm, called polynomial time algorithm, and the problem that can be solved by polynomial algorithm is P problem. There is another type of problem that has the following commonalities from the point of view of the computational complexity of the solution: 1 None of them find a polynomial algorithm. 2 If there is a polynomial algorithm for one of the problems, all problems in this category also have polynomial algorithms. The equivalence classes composed of these problems are called NP-complete problems such as packing problems and salesman problems. People often use "heuristic" algorithms to solve such problems, and can't guarantee to find the optimal solution, but often they can get better approximate solutions.