均匀容能设施选址问题的lp逼近

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Discrete Optimization Pub Date : 2022-08-01 DOI:10.1016/j.disopt.2022.100723
Sapna Grover , Neelima Gupta , Samir Khuller
{"title":"均匀容能设施选址问题的lp逼近","authors":"Sapna Grover ,&nbsp;Neelima Gupta ,&nbsp;Samir Khuller","doi":"10.1016/j.disopt.2022.100723","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by </span>rounding a solution to the standard LP with a slight </span><span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math></span> violation in the capacities.</p><p>Our result shows that the standard LP is not too bad.</p><p>Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.</p><p>The result is also extended to give the first approximation for uniform hard capacitated <span><math><mi>k</mi></math></span>-facility location problem violating the capacities by a factor of <span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math></span> and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of <span><math><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mo>+</mo><mi>ϵ</mi></mrow></mfrac></math></span>.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"LP-based approximation for uniform capacitated facility location problem\",\"authors\":\"Sapna Grover ,&nbsp;Neelima Gupta ,&nbsp;Samir Khuller\",\"doi\":\"10.1016/j.disopt.2022.100723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span>In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by </span>rounding a solution to the standard LP with a slight </span><span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math></span> violation in the capacities.</p><p>Our result shows that the standard LP is not too bad.</p><p>Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.</p><p>The result is also extended to give the first approximation for uniform hard capacitated <span><math><mi>k</mi></math></span>-facility location problem violating the capacities by a factor of <span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math></span> and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of <span><math><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mo>+</mo><mi>ϵ</mi></mrow></mfrac></math></span>.</p></div>\",\"PeriodicalId\":50571,\"journal\":{\"name\":\"Discrete Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572528622000330\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528622000330","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1

摘要

本文研究了均匀硬容设施选址问题。已知该问题的标准LP具有无界的完整性间隙。我们通过在容量中有轻微(1+ λ)违反的标准LP的解进行四舍五入,提出常数因子近似。我们的结果表明,标准LP并不差。与使用效率低下的椭球方法和分离预言器的基于强化lp的真近似相比,我们的算法简单有效。真正的近似也因使用局部搜索技术而受到收敛问题的困扰而闻名。此外,基于标准LP的解决方案更容易与其他基于LP的算法集成。结果也得到了推广,给出了一致硬容化k-设施定位问题的第一个近似,该问题违反容量的系数为(1+ λ),并且在容量违反中打破了2的障碍。结果违背了基数性的一个因子(21+ λ)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
LP-based approximation for uniform capacitated facility location problem

In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by rounding a solution to the standard LP with a slight (1+ϵ) violation in the capacities.

Our result shows that the standard LP is not too bad.

Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.

The result is also extended to give the first approximation for uniform hard capacitated k-facility location problem violating the capacities by a factor of (1+ϵ) and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of 21+ϵ.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
期刊最新文献
Anchor-robust project scheduling with non-availability periods Circuit and Graver walks and linear and integer programming Approximation schemes for Min-Sum k-Clustering Easy and hard separation of sparse and dense odd-set constraints in matching Mostar index and bounded maximum degree
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1