Finding a subset of nonnegative vectors with a coordinatewise large sum

被引：0
|
作者：
Bogdanov, Ilya I. [1 ,2 ]
Chelnokov, Grigory R. [2 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Reg, Russia
[2] Yaroslavl State Univ, Lab Discrete & Computat Geometry, Yaroslavl 150000, Russia
来源：
DISCRETE MATHEMATICS | 2013年 / 313卷 / 05期
关键词：
Subsum optimization; Linear programming;
D O I：
10.1016/j.disc.2012.12.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a rational a = p/q and N nonnegative d-dimensional real vectors u(1,) ..., u(N), we show that it is always possible to choose (d - 1) + inverted right perpendicular(pN - d + 1)/qinverted left perpendicular of them such that their sum is (componentwise) at least (p/q)(u(1) + ... + u(N)). For fixed d and a, this bound is sharp if N is large enough. The method of the proof uses Caratheodory's theorem from linear programming. (C) 2012 Elsevier B.V. All rights reserved.
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页码：622 / 625
页数：4
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