A network improvement problem under different norms

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	A network improvement problem under different norms
	Zhang, JZ ; Yang, XG ; Cai, MC
	2004-03-01
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
卷号	27 期号:3 页码:305-319
摘要	In this paper, we first consider a network improvement problem, called vertex-to-vertices distance reduction problem. The problem is how to use a minimum cost to reduce lengths of the edges in a network so that the distances from a given vertex to all other vertices are within a given upper bound. We use l(infinity), l(1) and l(2) norms to measure the total modification cost respectively. Under l(infinity) norm, we present a strongly polynomial algorithm to solve the problem, and under l(1) or weighted l(2) norm, we show that achieving an approximation ratio O( log(\|V\|)) is NP-hard. We also extend the results to the vertex-to-points distance reduction problem, which is to reduce the lengths of edges most economically so that the distances from a given vertex to all points on the edges of the network are within a given upper bound.
关键词	network improvement problems location problem strongly polynomial algorithms inapproximability
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000188330900005
出版者	KLUWER ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1015
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, JZ
作者单位	1.City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, JZ,Yang, XG,Cai, MC. A network improvement problem under different norms[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2004,27(3):305-319.
APA	Zhang, JZ,Yang, XG,&Cai, MC.(2004).A network improvement problem under different norms.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,27(3),305-319.
MLA	Zhang, JZ,et al."A network improvement problem under different norms".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 27.3(2004):305-319.