1998
DOI: 10.1007/3-540-49481-2_6
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Optimized Q-pivot for Exact Linear Solvers

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Cited by 5 publications
(2 citation statements)
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“…More precisely, as Espinoza (2006) demonstrates computationally, the running time of the naïve approach is not so much correlated with the size of an LP, but with the encoding length of the basic solutions traversed by the simplex algorithm. Notable improvements of this approach are Edmonds' Q-pivoting (see Edmonds (1994), Edmonds and Maurras (1997), Azulay and Pique (1998)) and the mixed-precision simplex algorithm of Gärtner (1999). Recent, more performant research efforts exploit the basis information provided by the simplex algorithm.…”
Section: Exact Methods For Linear Programming Over the Rational Numbersmentioning
confidence: 99%
“…More precisely, as Espinoza (2006) demonstrates computationally, the running time of the naïve approach is not so much correlated with the size of an LP, but with the encoding length of the basic solutions traversed by the simplex algorithm. Notable improvements of this approach are Edmonds' Q-pivoting (see Edmonds (1994), Edmonds and Maurras (1997), Azulay and Pique (1998)) and the mixed-precision simplex algorithm of Gärtner (1999). Recent, more performant research efforts exploit the basis information provided by the simplex algorithm.…”
Section: Exact Methods For Linear Programming Over the Rational Numbersmentioning
confidence: 99%
“…Edmonds noted that the inverse of a basis matrix can be represented as matrix of integer coefficients divided by a common denominator and that this representation can be efficiently updated when pivoting from basis to basis; this method is referred to as the Q-method and is further developed by [11] and [4]. Compared to computing a basis inverse with rational coefficients, the Q-method avoids the repeated GCD computations required by exact rational arithmetic.…”
Section: Methods For Exact Linear Programmingmentioning
confidence: 99%