Shortest path and maximum flow problems in networks with additive losses and gains

doi:10.1016/j.tcs.2010.11.019

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	Shortest path and maximum flow problems in networks with additive losses and gains
	Brandenburg, Franz J.1; Cai, Mao-cheng 2
	2011-02-04
发表期刊	THEORETICAL COMPUTER SCIENCE
ISSN	0304-3975
卷号	412 期号:4-5 页码:391-401
摘要	We introduce networks with additive losses and gains on the arcs. If a positive flow of x units enters an arc a, then x + g(a) units exit. Arcs may increase or consume flow, i.e., they are gainy or lossy. Such networks have various applications, e.g., in financial analysis, transportation, and data communication. Problems in such networks are generally intractable. In particular, the shortest path problem is NP-hard. However, there is a pseudo-polynomial time algorithm for the problem with nonnegative costs and gains. The maximum flow problem is strongly NP-hard, even in networks with integral capacities and with unit gain or with loss two on the arcs, and is hard to approximate. However, it is solvable in polynomial time in unit-loss networks using the Edmonds-Karp algorithm. Our NP-hardness results contrast efficient polynomial time solutions of path and flow problems in standard and in so-called generalized networks with multiplicative losses and gains. (c) 2010 Elsevier B.V. All rights reserved.
关键词	Extended networks Lossy and gainy arcs Max-flow problems Shortest path problems NP-hard problems Unit-loss networks
DOI	10.1016/j.tcs.2010.11.019
语种	英语
资助项目	Natural Science Foundation of China[10171054]
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000286862100012
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11257
专题	中国科学院数学与系统科学研究院
通讯作者	Brandenburg, Franz J.
作者单位	1.Univ Passau, D-94030 Passau, Germany 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Brandenburg, Franz J.,Cai, Mao-cheng. Shortest path and maximum flow problems in networks with additive losses and gains[J]. THEORETICAL COMPUTER SCIENCE,2011,412(4-5):391-401.
APA	Brandenburg, Franz J.,&Cai, Mao-cheng.(2011).Shortest path and maximum flow problems in networks with additive losses and gains.THEORETICAL COMPUTER SCIENCE,412(4-5),391-401.
MLA	Brandenburg, Franz J.,et al."Shortest path and maximum flow problems in networks with additive losses and gains".THEORETICAL COMPUTER SCIENCE 412.4-5(2011):391-401.