Algorithms for the metric ring star problem with fixed edge-cost ratio

doi:10.1007/s10878-019-00418-w

CSpace > 应用数学研究所

	Algorithms for the metric ring star problem with fixed edge-cost ratio
	Chen, Xujin1,2 ; Hu, Xiaodong1,2 ; Jia, Xiaohua 3; Tang, Zhongzheng1,2,3 ; Wang, Chenhao1,2,3 ; Zhang, Ying 4
	2021-10-01
发表期刊	JOURNAL OF COMBINATORIAL OPTIMIZATION
ISSN	1382-6905
卷号	42 期号:3 页码:499-523
摘要	We address the metric ring star problem with fixed edge-cost ratio, abbreviated as RSP. Given a complete graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V,E)$$\end{document} with a specified depot node d is an element of V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\in V$$\end{document}, a nonnegative cost function c is an element of R+E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c\in \mathbb {R}_+<^>E$$\end{document} on E which satisfies the triangle inequality, and an edge-cost ratio M >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge 1$$\end{document}, the RSP is to locate a ring R=(V ',E ')\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=(V',E')$$\end{document} in G, a simple cycle through d or d itself, aiming to minimize the sum of two costs: the cost for constructing ring R, i.e., M center dot n-ary sumation e is an element of E ' c(e)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\cdot \sum _{e\in E'}c(e)$$\end{document}, and the cost for attaching nodes in V\V '\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V{\setminus } V'$$\end{document} to their closest ring nodes (in R), i.e., n-ary sumation u is an element of V\V ' minv is an element of V ' c(uv)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{u\in V{\setminus } V'}\min _{v\in V'}c(uv)$$\end{document}. We show that the singleton ring d is an optimal solution of the RSP when M >=(\|V\|-1)/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge (\|V\|-1)/2$$\end{document}. This particularly implies a \|V\|-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{\|V\|-1}$$\end{document}-approximation algorithm for the RSP with any M >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge 1$$\end{document}. We present randomized 3-approximation algorithm and deterministic 5.06-approximation algorithm for the RSP, by adapting algorithms for the tour-connected facility location problem (tour-CFLP) and single-source rent-or-buy problem due to Eisenbrand et al. and Williamson and van Zuylen, respectively. Building on the PTAS of Eisenbrand et al. for the tour-CFLP, we give a PTAS for the RSP with \|V\|/M=O(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\|V\|/M=O(1)$$\end{document}. We also consider the capacitated RSP (CRSP) which puts an upper limit k on the number of leaf nodes that a ring node can serve, and present a (10+6M/k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(10+6M/k)$$\end{document}-approximation algorithm for this capacitated generalization. Heuristics based on some natural strategies are proposed for both the RSP and CRSP. Simulation results demonstrate that the proposed approximation and heuristic algorithms have good practical performances.
关键词	Ring star Approximation algorithms Heuristics Local search Connected facility location
DOI	10.1007/s10878-019-00418-w
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Interdisciplinary Applications ; Mathematics, Applied
WOS记录号	WOS:000712986900010
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59540
专题	应用数学研究所
通讯作者	Wang, Chenhao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.City Univ Hong Kong, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China 4.Beijing Elect Sci & Technol Inst, Beijing 100070, Peoples R China
推荐引用方式 GB/T 7714	Chen, Xujin,Hu, Xiaodong,Jia, Xiaohua,et al. Algorithms for the metric ring star problem with fixed edge-cost ratio[J]. JOURNAL OF COMBINATORIAL OPTIMIZATION,2021,42(3):499-523.
APA	Chen, Xujin,Hu, Xiaodong,Jia, Xiaohua,Tang, Zhongzheng,Wang, Chenhao,&Zhang, Ying.(2021).Algorithms for the metric ring star problem with fixed edge-cost ratio.JOURNAL OF COMBINATORIAL OPTIMIZATION,42(3),499-523.
MLA	Chen, Xujin,et al."Algorithms for the metric ring star problem with fixed edge-cost ratio".JOURNAL OF COMBINATORIAL OPTIMIZATION 42.3(2021):499-523.