Match making assignments based on bilateral preferences

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Since the coordinate value is integer number generally, involves floating computing if. It is a form of geometry in which the distance between two points is the sum of the absolute differences of their Cartesian coordinate value. The origin of coordinates is the central point of this quadrate, and the length of its each side is ; meanwhile each side is parallel with coordinate axes.
If has the same preference degree as some elements in or , we label them with parentheses. The four matrixes , , , and are presented as follows: The structure of the set of stable matchings. The main idea of branch-and-bound algorithm is to increase lower bound and decrease upper bound iteratively and get the optimal value finally.

Mathematical Problems in Engineering

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We define the preference sequence of an element in one set as a certain preference sequence only when all the elements in the other set have direct and certain ordinal value in accordance with this sequence; otherwise it is an uncertain preference sequence. It is first proposed by Land and Doig in for discrete programming [ 23 ] and has become the most commonly used tool for solving integer programming and NP-hard problem.
The focus of the book is Selected pages Title Page. What socially desirable properties they should have? Introduction Two-sided matching is an important research branch in the field of operation research and decision analysis, which has been applied into many aspects of engineering and economics, such as commerce trading [ 1 , 2 ], work assignment [ 3 , 4 ], and resource allocation [ 5 , 6 ]. Meanwhile, Solution also has the least total sum of disagreements of two sides. Keeping college admission institutions in mind, these problems are described as follows.
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