Thresholded covering algorithms for robust and max–min optimization
Thresholded covering algorithms for robust and max–min optimization
复制标题
用于稳健和最大最小优化的阈值覆盖算法
DOI：
10.1007/s10107-013-0705-5
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发表时间：
2009
影响因子：
2.7
通讯作者：
R. Ravi
中科院分区：
文献类型：
--
作者：
Anupam Gupta;V. Nagarajan;R. Ravi
在两个阶段的强大涵盖问题中，明天将出现几种可能的情况之一，但要覆盖的费用高于今天您应该购买的明天。 ）最小化吗？ \ use-package {upgreek} \ setLength {\ oddSideMargin} { - 69pt} \ begin {document} $ k $$ k $$ k $$ \ end {document {document} -Robust模型，明天可能会在所有需求k \ document-document-ubssets给出了可能的方案。 [12pt] {minimal} \ usepackage {amsmath} \ usepackage {asysym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amsymb} \ usepackage Argin} { - 69pt } \ begin {document} $$ k $$ \ end {document}。 {amsfonts} \ usepackage {amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ usepackage {upgreek} \ setLength涵盖问题：建立了一些预期解决方案，如果有存在一个单一的需求，其增强成本大于某些阈值，增强了预期解决方案以涵盖此需求，然后重复说明，该模板为K \ DocumentClass提供了良好的近似算法[12pt] {Minimal} \ usepackage } \ usepackage {wasySym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ begin {document} $$ k $$ \ end {document {document} - 许多标准覆盖问题的抢劫版本：设置封面，施泰纳树，施泰纳森林，最小切割和我们的k \ documentclass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasysym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amsbsy} \ begin {document} $ $ k $$ \ end {document} - 抛光近似比率几乎与确定性的最佳界限相匹配。 。 \ use-package {amsfonts} \ usepackage {amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ usepackage {usepackage {upgreek} \ upgreek} \ setLength对于上述问题，我们表明他们的k \ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasySym} \ useym} \ usepackage {amsfonts} {amsbsy} \ usepackage {mathrsfs} \ use-package {upgreek} \ setLength {\ oddSideMargin} { - 69pt} \ begin {document} $$ k $$ k $ j $ ten {document} -max-min版本的性能保证与K \ documentclass [12pt] {12pt] {最小值} \ usepackage {amsmath} \ usepackage {wasysym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amsmb} -69pt} \ begin {文档} $$ k $$ \ end {document} - 抢劫问题。
In a two-stage robust covering problem, one of several possible scenarios will appear tomorrow and require to be covered, but costs are higher tomorrow than today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? We consider the k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-robust model where the possible scenarios tomorrow are given by all demand-subsets of size k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}. In this paper, we give the following simple and intuitive template for k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-robust covering problems: having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat. We show that this template gives good approximation algorithms for k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-robust versions of many standard covering problems: set cover, Steiner tree, Steiner forest, minimum-cut and multicut. Our k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-robust approximation ratios nearly match the best bounds known for their deterministic counterparts. The main technical contribution lies in proving certain net-type properties for these covering problems, which are based on dual-rounding and primal–dual ideas; these properties might be of some independent interest. As a by-product of our techniques, we also get algorithms for max–min problems of the form: “given a covering problem instance, whichk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}of the elements are costliest to cover?” For the problems mentioned above, we show that their k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-max–min versions have performance guarantees similar to those for the k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-robust problems.