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- W2065184613 abstract "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 $C={ensuremath{sum}}_{i<j}{C}_{ij}({I}_{ij})$, with ${C}_{ij}text{ }({I}_{ij})$ 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 ${C}_{ij}ensuremath{propto}{|{I}_{ij}|}^{ensuremath{gamma}}$ with $0<ensuremath{gamma}<1$. 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." @default.
- W2065184613 created "2016-06-24" @default.
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- W2065184613 date "2007-06-27" @default.
- W2065184613 modified "2023-09-26" @default.
- W2065184613 title "Optimal transportation network with concave cost functions: Loop analysis and algorithms" @default.
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- W2065184613 doi "https://doi.org/10.1103/physreve.75.066112" @default.
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