However, fast calculation methods based on integer programming allow a computation time in seconds for some cases with as many as 40 choices.
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A particularly fast method for exact BN learning is to cast the problem as an optimisation problem, and solve it using Integer programming.
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For example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions.
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M�bius ladders have also been used in computer science, as part of integer programming approaches to problems of set packing and linear ordering.
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The many applications of the algorithmic theory of Graver bases also include stochastic integer programming, clustering, and disclosure control in statistical databases.
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Lenstra in 1983 showed that, when the number of variables is fixed, the feasibility integer programming problem can be solved in polynomial time.
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Integer programming is the problem of optimizing a linear or nonlinear objective function over the set of integer points satisfying a system of linear inequalities.
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Thus systems of linear Diophantine equations are basic in this context, and textbooks on integer programming usually have a treatment of systems of linear Diophantine equations.
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MINTO ( Mixed Integer Optimizer, an integer programming solver which uses branch and bound algorithm ) has publicly available source code but is not open source.
30.
It has been reported that calculation methods based on integer programming sometimes allowed the computation of full rankings for votes on as many as 40 candidates in seconds.
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