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Integer Linear Programming in Computational Biology
2009Computational molecular biology (bioinformatics) is a young research field that is rich in NP-hard optimization problems. The problem instances encountered are often huge and comprise thousands of variables. Since their introduction into the field of bioinformatics in 1997, integer linear programming (ILP) techniques have been successfully applied to ...
Ernst Althaus +4 more
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Termination of Integer Linear Programs
2006We show that termination of a simple class of linear loops over the integers is decidable. Namely we show that termination of deterministic linear loops is decidable over the integers in the homogeneous case, and over the rationals in the general case. This is done by analyzing the powers of a matrix symbolically using its eigenvalues.
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A Note on Linear Programming and Integer Feasibility
Operations Research, 1968This paper proves a theorem that provides new strategies for solving integer programming problems, based on finding certain types of basic solutions to linear programs. The theorem is motivated by and extends ideas of Cabot and Hurter. An integer programming method based on the theorem is outlined.
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Linear and Integer Programming
2016Integer Programming (IP) is a modelling tool that has been widely applied in the last decades to obtain solutions for complex real problems, as those that arise in cutting and packing, location, routing and many other areas.
Cláudio Alves +3 more
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An Integer Programming Problem with a Linear Programming Solution
The American Mathematical Monthly, 20001995. 12. Paul Halmos and Steven Givant, Logic as Algebra, Dolciani Mathematical Expositions-No. 21, The Mathematical Association of America, Washington, D.C., 1998. 13. I. N. Herstein, Topics in Algebra, Xerox College Publishing, Lexington, Mass., 1964 (also: Wiley, New York, 1975). 14.
Kevin A. Broughan, Nan Zhu
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Comparison between linear programming and integer linear programming: a review
International Journal of Mathematics in Operational Research, 2018This research discusses comparison of linear programming (LP) and integer linear programming (ILP). Two techniques to solve LP, simplex method and interior-point method were introduced. For ILP, available algorithms can be classified into exact algorithms and heuristic algorithms.
Mei Lee Sam +3 more
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An integer programming approach for linear programs with probabilistic constraints
Mathematical Programming, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James R. Luedtke +2 more
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Watermarking integer linear programming solutions
Proceedings of the 39th conference on Design automation - DAC '02, 2002Linear programming (LP) in its many forms has proven to be an indispensable tool for expressing and solving optimization problems in numerous domains. We propose the first set of generic watermarking techniques for integer-LP (ILP). The proof of authorship by watermarking is achieved by introducing additional constraints to limit the solution space and
Seapahn Megerian +2 more
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Sensitivity theorems in integer linear programming
Mathematical Programming, 1986This is an important paper, with a number of highly significant results. The issues surround integer linear programs with fixed coefficient matrices, and varying objective functions and right-hand side vectors. This work strengthens, implies, generalizes and/or strongly relates to work by Blair and Jeroslow, Graver, Wolsey, Gomory, von zur Gathen and ...
William J. Cook +3 more
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Optima of dual integer linear programs
Combinatorica, 1988Let \(A\) be a 0-1 matrix of dimension \(n\cdot m\). Consider the following pair of linear programs \[ \text{(L)}\quad \max x\cdot 1,\quad Ax\leq 1,\quad x\geq 0;\quad \text{(D)}\quad \min y\cdot 1,\quad yA\geq 1,\quad y\geq 0. \] If integral solution constraints are added, they become dual pairs of packing and covering integer linear programs. Let \(z\
Ron Aharoni, Paul Erdös, Nathan Linial
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