FPT-algorithms for some problems related to integer programming

被引：4
|
作者：
Gribanov, D. V. [1 ,2 ]
Malyshev, D. S. [2 ]
Pardalos, P. M. [2 ,3 ]
Veselov, S. I. [1 ]
机构：
[1] Lobachevsky State Univ Nizhny Novgorod, 23 Gagarina Ave, Nizhnii Novgorod 603950, Russia
[2] Natl Res Univ Higher Sch Econ, 25-12 Bolshaja Pecherskaja Ulitsa, Nizhnii Novgorod 603155, Russia
[3] Univ Florida, 401 Weil Hall,POB 116595, Gainesville, FL 32611 USA
来源：
JOURNAL OF COMBINATORIAL OPTIMIZATION | 2018年 / 35卷 / 04期
基金：
俄罗斯科学基金会; 俄罗斯基础研究基金会;
关键词：
Integer programming; Shortest lattice vector problem; Matrix minors; FPT-algorithm; Lattice width; STRONGLY POLYNOMIAL ALGORITHM; TIME ALGORITHM; LATTICE; VECTORS; COMPLEXITY;
D O I：
10.1007/s10878-018-0264-z
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms with respect to the same parameter for the problems, when the matrices have no singular rank submatrices.
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页码：1128 / 1146
页数：19
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