An improved lower bound for approximating the Minimum Integral Solution Problem with Preprocessing over norm

被引：0

作者：

Chen, Wenbin ^{[1
,2
,3
]}

Peng, Lingxi ^{[1
]}

Wang, Jianxiong ^{[1
]}

Li, Fufang ^{[1
]}

Tang, Maobin ^{[1
]}

Xiong, Wei ^{[1
]}

Wang, Songtao ^{[4
]}

机构：

[1] Guangzhou Univ, Dept Comp Sci, Guangzhou, Guangdong, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China

[3] Nanjing Univ, State Key Lab Novel Software Technol, Nanjing 210008, Jiangsu, Peoples R China

[4] S China Normal Univ, Guangzhou, Guangdong, Peoples R China

来源：

JOURNAL OF COMBINATORIAL OPTIMIZATION | 2015年 / 30卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Minimum Integral Solution Problem; Computational complexity; NP-hardness; PCP; CLOSEST VECTOR PROBLEM; CODING PROBLEMS; HARDNESS; INAPPROXIMABILITY; LATTICE; CODES;

D O I：

10.1007/s10878-013-9646-4

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 study the approximation complexity of the Minimum Integral Solution Problem with Preprocessing introduced by Alekhnovich et al. (FOCS, pp. 216-225, 2005). We show that the Minimum Integral Solution Problem with Preprocessing over norm () is NP-hard to approximate to within a factor of unless This improves on the best previous result. The best result so far gave factor hardness for any epsilon > 0.

引用

页码：447 / 455

页数：9

共 50 条

[1] Inapproximability results for the minimum integral solution problem with preprocessing over l∞ norm
Chen, Wenbin
Peng, Lingxi
Wang, Jianxiong
Li, Fufang
Tang, Maobin
Xiong, Wei
Wang, Songtao
[J]. THEORETICAL COMPUTER SCIENCE, 2013, 478 : 127 - 131
[2] An improved lower bound for approximating minimum GCD multiplier in l∞ norm (GCDM∞)
Chen, WenBin
Meng, Jiangtao
Yin, Dengpan
[J]. THEORETICAL COMPUTER SCIENCE, 2008, 396 (1-3) : 1 - 9
[3] An improved lower bound for approximating Shortest Integer Relation in l∞ norm (SIR∞)
Chen, Wenbin
Meng, Jiangtao
[J]. INFORMATION PROCESSING LETTERS, 2007, 101 (04) : 174 - 179
[4] AN IMPROVED LOWER BOUND TO THE MINIMUM FLEET SIZE PROBLEM
STERN, HI
CEDER, A
[J]. TRANSPORTATION SCIENCE, 1983, 17 (04) : 471 - 477
[5] An improved lower bound for approximating the Minimum Integral Solution Problem with Preprocessing over ℓ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _\infty $$\end{document} norm
Wenbin Chen
Lingxi Peng
Jianxiong Wang
Fufang Li
Maobin Tang
Wei Xiong
Songtao Wang
[J]. Journal of Combinatorial Optimization, 2015, 30 (3) : 447 - 455
[6] A lower bound for approximating the geometric minimum weight matching
Das, G
Smid, M
[J]. INFORMATION PROCESSING LETTERS, 2000, 74 (5-6) : 253 - 255
[7] Improved Bound on Approximating Jug Measuring Problem
Shieh, Min-Zheng
Tsai, Shi-Chun
[J]. JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, 2011, 27 (03) : 1159 - 1163
[8] The hardness of the closest vector problem with preprocessing over l∞ norm
Chen, Wenbin
Meng, Jiangtao
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (10) : 4603 - 4606
[9] An integral equations method combined minimum norm solution for 3D elastostatics Cauchy problem
Sun, Yao
Ma, Fuming
Zhang, Deyue
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 271 : 231 - 252
[10] Approximating the minimum strongly connected subgraph via a matching lower bound.
Vetta, A
[J]. PROCEEDINGS OF THE TWELFTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2001, : 417 - 426

← 1 2 3 4 5 →