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Phys Rev E. 2016 Mar;93(3):032321. doi: 10.1103/PhysRevE.93.032321. Epub 2016 Mar 25.

Optimal transport in time-varying small-world networks.

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Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China.
School of Information Science and Technology, East China Normal University, Shanghai 200241, China.
School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China.
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China.


The time-order of interactions, which is regulated by some intrinsic activity, surely plays a crucial role regarding the transport efficiency of transportation systems. Here we study the optimal transport structure by measure of the length of time-respecting paths. Our network is built from a two-dimensional regular lattice, and long-range connections are allocated with probability P(ij)∼r(ij)(-α), where r(ij) is the Manhattan distance. By assigning each shortcut an activity rate subjected to its geometric distance τ(ij)∼r(ij)(-C), long-range links become active intermittently, leading to the time-varying dynamics. We show that for 0<C<2, the network behaves as a small world with an optimal structural exponent α(opt) that slightly grows with C as α(opt)∼log(C), while for C ≫ 2 the α(opt)→∞. The unique restriction between C and α unveils an optimization principle in time-varying transportation networks. Empirical studies on British Airways and Austrian Airlines provide consistent evidence with our conclusion.


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