OPTIMAL TEMPORAL PATH ON SPATIAL DECAYING NETWORKS

We introduce temporal effect to the classical Kleinberg model and study how it affects the spatial structure of optimal transport network. The initial network is built from a regular d-dimensional lattice added by shortcuts with probability p(r(ij)) similar to r(ij)(-alpha), where r(ij) is the geometric distance between node i and j. By assigning each shortcut an energy E = r.tau, a link with length r survives within period tau, which leads the network to a decaying dynamics of constantly losing long-range links. We find new optimal transport in the dynamical system for alpha = 43d, in contrast to any other result in static systems. The conclusion does not depend on the information used for navigation, being based on local or global knowledge of the network, which indicates the possibility of the optimal design for general transport dynamics in the time-varying network.