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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
Source PublicationPHYSICAL REVIEW E
KeywordComplex Networks Evolution Energy
AbstractTransportation 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.
2007
ISSN1539-3755
Volume75Issue:6Pages:-
Subject AreaPhysics
Indexed BySCI
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/5722
Collection理论物理所科研产出_SCI论文
Corresponding AuthorShao, Z , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
Recommended Citation
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):-.
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