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Integer programming with 2-variable equations and 1-variable inequalities

2009
*
Information Processing Letters
*

We present an efficient algorithm to find an optimal

doi:10.1016/j.ipl.2009.01.025
fatcat:vdbn6o2blfgjvafq6dbr2q2uwa
*integer*solution of a given system of*2*-*variable*equalities*and**1*-*variable**inequalities**with*respect to a given linear objective function. ... Our algorithm has worst-case running time in O(N*2*) where N is the number of bits in the input. ... Again it should be clear (by similar reasoning as in the previous sections) that the necessary computations can be done in O(N*2*) time. ...##
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A Novel Alternative Algorithm for Solving Linear Integer Programming Problems with Four Variables

2021
*
European Journal of Science and Technology
*

In this paper, new iterative method is proposed based on parametrization for solving

doi:10.31590/ejosat.1020212
fatcat:sjaqmcpjmbe2hjco6umxuza7um
*Integer*Linear*Programming*(ILP) problems*with*four*variables**and*an algorithm is provided. ... Our method, which is better than the cutting plane method*and*branch*and*bound methods in solving ILP problems*with*four*variables*, can be easily applied regardless of the number of constraints. ...*Inequalities**with*respect to the point (𝑦*1*, 𝑦 3 ) 𝑥*1*Avrupa Bilim ve Is there at least one*integer*point (𝑦*1*, 𝑦 3 ) satisfyin g the*inequality*? Is 𝑦*2*an*integer*? ...##
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AN ALGORITHM FOR SOLVING INTEGER LINEAR PROGRAMMING PROBLEMS

2013
*
International Journal of Research in Engineering and Technology
*

The two main proposals for solving

doi:10.15623/ijret.2013.0207012
fatcat:qfzo5hjonjgzdktcmsp3laigua
*integer*linear*programming*problems are those of Gomory [*1*]*and*Land*and*Doig [*2*. The method of Gomory starts*with*the simplex solution. ... This elimination process can now be repeated*with**2*, 3' etc., until finally, one arrives at a set of Nn-*2**inequalities*involving a -single*variable*n-*1*. ...##
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Parametric Strategy Iteration
[article]

2014
*
arXiv
*
pre-print

Parametric strategy iteration for systems of

arXiv:1406.5457v1
fatcat:rake6of3ovg5fgbzgkt6nn2mny
*integer**equations*allows to construct parametric*integer*interval analysis as well as parametric analysis of differences of*integer**variables*. ... It thus provides a general technique to realize precise parametric*program*analysis if numerical properties of*integer**variables*are of concern. ... We thank Stefan Barth (LMU) for Example 4,*and*Jan Reineke (Universität des Saarlandes) for useful discussions. ...##
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Propagating dense systems of integer linear equations

2007
*
Proceedings of the 2007 ACM symposium on Applied computing - SAC '07
*

We show on standard

doi:10.1145/1244002.1244075
dblp:conf/sac/FeydyS07
fatcat:ckstu2cpezcnpd5nl7fvjo2dn4
*integer*benchmarks how these new propagators can substantially improve propagation performance, in terms of strength of propagation*and*speed. ... In interval propagation approaches to solving non-linear constraints over reals it is common to build stronger propagators from systems of linear*equations*. ...*and*n*variables*will result in a system of m*equations*, each*with*(n − m) +*1*non quasi-zero coefficients. ...##
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DIV, FLOOR, CEIL, MOD and STEP Functions in Nested Loop Programs and Linearly Bounded Lattices
[chapter]

1995
*
Algorithms and Parallel VLSI Architectures III
*

The nested loop

doi:10.1016/b978-044482106-5/50024-7
fatcat:p7dbrrolsbeuvdmhf3my22t7zm
*programs*may contain the*integer*operators:*integer*division, floor, ceil,*and*modulo, in expressions*and*the stride, or step size, of for loops may be greater than one. ... We will show the relation between the*integer*division operators in the SAP*and*linearly bounded lattices in the corresponding DG. ... The domain of lattice offsets is formed by a polytope in*variables*of Ã . The polytope is characterized by matrix ½*and**inequalities*of the*variables*standing for the*integer*divisions. ...##
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Geometric Programming with Discrete Variables Subject to Max-Product Fuzzy Relation Constraints

2018
*
Discrete Dynamics in Nature and Society
*

The problem of geometric

doi:10.1155/2018/1610349
fatcat:cbv2o5ymfzeebpau6gfntrtcne
*programming*subject to max-product fuzzy relation constraints*with*discrete*variables*is studied. ... We proposed a 0-*1*mixed*integer*linear*programming*model*and*adopted the branch-*and*-bound scheme to solve the problem. Numerical experiments confirm that the proposed solution method is effective. ... Acknowledgments This work has been supported by the Nature Science Foundation of Guangdong Province (nos. 2016A030307037, 2016A030313552,*and*QD20171001). ...##
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A Sequent Calculus for Integer Arithmetic with Counterexample Generation

2007
*
Conference on Automated Deduction
*

There are four main components: a complete procedure for linear

dblp:conf/cade/Rummer07
fatcat:t23aqt7sfbfobdoul6fha32iqm
*equations*, a complete procedure for linear*inequalities*, an incomplete procedure for nonlinear (polynomial)*equations*,*and*an incomplete ... The method is tailored to Java*program*verification*and*meant to be used both as a supporting procedure*and*simplifier during interactive verification*and*as an automated tool for discharging (ground) ... I want to thank Wolfgang Ahrendt*and*Richard Bubel for many inspiring discussions*and*comments on this paper. Thanks are also due to the anonymous referees for helpful comments. ...##
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The Elimination of Integer Variables

1992
*
Journal of the Operational Research Society
*

one all-

doi:10.1057/jors.1992.65
fatcat:dkogfv5tivh5vftn66vazk23qq
*integer**inequality*row (*2*)*with*entries in other rows (*2*) all being 0, negative or +*1*; or (iii) it has an entry —*1*in at least one all-*integer**inequality*row (*2*)*with*entries in other rows (*2*) ... Also, we can divide through these*inequalities*by the relevant non-zero coefficients giving*1*n iq j=0 JS#q*1*-*1*(> - > au 2X, kel Ang j=0 J#q together*with*(*1*)*and**inequalities*(*2*) in which x, has no ...##
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Integer Programming and Pricing

1960
*
Econometrica
*

method, starting

doi:10.2307/1910130
fatcat:e2fkqkjvj5g6vmgziipekr7raa
*with*the*integer**inequalities*in n a*,o + E a*, (-x>) (aO,j*integers*), J=*1*one introduces slack*variables*x', one for each*inequality*, converting them into*equations*n (i.*2*) x/ a= a* ... It is derived from an*equation*n ai,o + I ai,*1*(-t1)*1*=*1*where the*variables*, t, are either x's or slack*variables*of the original problem. ... Now the expression for the*variables*in terms of the non-basic set x' is unique, so all the coefficients must be identical*with*those obtained in solving the n*inequalities*of an ordinary linear*programming*...##
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A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables

2020
*
Cybernetics and Information Technologies
*

This method, which is better than the cutting plane

doi:10.2478/cait-2020-0045
fatcat:urcnikbz5fewdih6c5mzgaaxli
*and*branch boundary method, can be applied to pure*integer*linear*programming*problems*with*m linear*inequality*constraints, a linear objective function ...*with*three*variables*. ... It has an*integer*solution if*and*only if ; also, if a linear Diophantine*equation*has an*integer*solution; then there will be infinitely many solution for this*equation*[*1*] . ...##
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Propagating systems of dense linear integer constraints

2008
*
Constraints
*

In interval propagation approaches to solving nonlinear constraints over reals it is common to build stronger propagators from systems of linear

doi:10.1007/s10601-008-9049-9
fatcat:x3sx3tpw4bdxnatnoychq7r7gy
*equations*. ... In a similar fashion we present an interval Fourier elimination preconditioning technique to generate redundant linear constraints from a system of linear*inequalities*. ... Example 5 Consider the*integer**variables*x1, x2, x3,*with*the domains d1 = d2 = d3 = [−10, 10],*and*the following linear constraints: C1 :*2*4 5 3 4 −*1**2*−*2**1*−*1**2*3 5*2*4 x1 x2 x3 3 5 =*2*4 0 7 −*2*3 ...##
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The general form of 0–1 programming problem based on DNA computing

2003
*
Biosystems (Amsterdam. Print)
*

In this paper, we solved the general form of 0-

doi:10.1016/s0303-2647(03)00053-4
pmid:12753938
fatcat:qztoa5vmkzahrif33hzpjqrcuu
*1**programming*problem*with*fluorescence labeling techniques based on surface chemistry by attempting to apply DNA computing to a*programming*problem. ... Up to now, many accomplishments have been made to improve its performance*and*increase its reliability. ... They also wish to thank an anonymous referee of this paper who provided many useful*and*constructive suggestions for the improvement of this paper. ...##
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Mixed integer polynomial programming

2015
*
Computers and Chemical Engineering
*

The mixed

doi:10.1016/j.compchemeng.2014.07.020
fatcat:pt7rpsmdjzfs7px5ba75islje4
*integer*polynomial*programming*problem is reformulated as a multi-parametric*programming*problem by relaxing*integer**variables*as continuous*variables**and*then treating them as parameters. ... solution as a function of the relaxed*integer**variables*. ... Acknowledgments This paper is dedicated to Professor Ignacio Grossmann in celebration of his 65th birthday*and*in acknowledgement of his contributions to the field of Process Systems Engineering. ...##
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Fourier-Motzkin elimination extension to integer programming problems

1976
*
Journal of combinatorial theory. Series A
*

deal

doi:10.1016/0097-3165(76)90055-8
fatcat:aeynivmfwnd3rjo3k2ty6rcck4
*with**Integer**Programming*(IP) problems. ... This paper describes how the Fourier-Motzkin Elimination Method, which can be used for solving Linear*Programming*Problems, can be extended to deal*with**Integer**Programming*Problems. ...*with**Integer**Programming*Problems. ...
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