Optimal transportation network with concave cost functions: Loop analysis and algorithms

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	Optimal transportation network with concave cost functions: Loop analysis and algorithms
	Shao, Zhen; Zhou, Haijun; Shao, Z , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
刊名	PHYSICAL REVIEW E
	2007
卷号	75 期号:6 页码:-
关键词	Complex Networks Evolution Energy
ISSN号	1539-3755
英文摘要	Transportation networks play a vital role in modern societies. Structural optimization of a transportation system under a given set of constraints is an issue of great practical importance. For a general transportation system whose total cost C is determined by C=Sigma C-i < j(ij)(I-ij), with C-ij (I-ij) being the cost of the flow I-ij between node i and node j, Banavar and co-workers [Phys. Rev. Lett. 84, 4745 (2000)] proved that the optimal network topology is a tree if C-ij proportional to parallel to I-ij parallel to(gamma) with 0 < 1. The same conclusion also holds in the more general case where all the flow costs are strictly concave functions of the flow I-ij. To further understand the qualitative difference between systems with concave and convex cost functions, a loop analysis of transportation cost is performed in the present paper, and an alternative mathematical proof of the optimality of tree-formed networks is given. The simple intuitive picture of this proof then leads to an efficient global algorithm for the searching of optimal structures for a given transportation system with concave cost functions.
学科主题	Physics
URL标识	查看原文
WOS记录号	WOS:000247624100019
公开日期	2012-08-02
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/5722]
专题	理论物理研究所_理论物理所1978-2010年知识产出
通讯作者	Shao, Z , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Shao, Zhen,Zhou, Haijun,Shao, Z , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China. Optimal transportation network with concave cost functions: Loop analysis and algorithms[J]. PHYSICAL REVIEW E,2007,75(6):-.
APA	Shao, Zhen,Zhou, Haijun,&Shao, Z , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China.(2007).Optimal transportation network with concave cost functions: Loop analysis and algorithms.PHYSICAL REVIEW E,75(6),-.
MLA	Shao, Zhen,et al."Optimal transportation network with concave cost functions: Loop analysis and algorithms".PHYSICAL REVIEW E 75.6(2007):-.