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Linear Programming with Two Variables per Inequality in PolyLog Time
 SIAM J. Computing
, 1990
"... The parallel time complexity of the linear programming problem with at most twovariables per inequality is discussed. Let m denote the number of variables and the number of inequalities, respectively,ina linear programming problem. We assume all inequalities are weak. We describe an O((log m ..."
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Cited by 4 (2 self)
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The parallel time complexity of the linear programming problem with at most twovariables per inequality is discussed. Let m denote the number of variables and the number of inequalities, respectively,ina linear programming problem. We assume all inequalities are weak. We describe an O((log
A PRACTICAL ALGORITHM for Exact Array Dependence Analysis
, 1992
"... A fundamental analysis step in advanced optimizing compiler (as well as many other software tools) is data dependence analysis for arrays. This means deciding if two references to an array can refer to the same element and if so, under what conditions. This information is used to determine allowabl ..."
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Cited by 196 (0 self)
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of integer programming. The problem as just shown would be formulated as an integer programming problem in the next example. In this example, iw andjw refer to the values of the loop variables at the time the write is performed and iT and jr refer to the values of the loop variables at the time the read
Tight Bounds and 2Approximation Algorithms for Integer Programs with Two Variables per Inequality
 Mathematical Programming
, 1992
"... . The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NPcomplete, even when all variables are binary. This paper deals with integer linear minimization problems in n variables subject to m linear constraints with at most tw ..."
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Cited by 45 (6 self)
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two variables per inequality, and with all variables bounded between 0 and U . For such systems, a 2\Gammaapproximation algorithm is presented that runs in time O(mnU 2 log(Un 2 =m)), so it is polynomial in the input size if the upper bound U is polynomially bounded. The algorithm works
Linear Matrix Inequalities.............
"... For contact information about worldwide offices, see the MathWorks Web site. ..."
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For contact information about worldwide offices, see the MathWorks Web site.
PER
"... Design and operation of power systems with large amounts of wind power IEA Wind Task 25 Final report, ..."
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Design and operation of power systems with large amounts of wind power IEA Wind Task 25 Final report,
Exact algorithms for linear matrix inequalities
, 2015
"... Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1,..., An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a line ..."
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linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on the input matrices, computes an exact algebraic representation of at least one point in the spectrahedron, or decides that it is empty. The algorithm does not assume the existence of an interior point
inequalities
, 1999
"... Exact nonlinear budget constraints determined by systems of equations and ..."
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Cited by 1 (0 self)
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Exact nonlinear budget constraints determined by systems of equations and
Results 1  10
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296,504