Options
Biased random walks on Kleinberg’s spatial networks
Author(s)
Date Issued
2016
Publisher
Elsevier BV
ISSN
0378-4371
1873-2119
Citation
Physica A: Statistical Mechanics and its Applications, 2016, vol. 463, pp. 509-515.
Type
Peer Reviewed Journal Article
Abstract
We investigate the problem of the particle or message that travels as a biased random walk toward a target node in Kleinberg’s spatial network which is built from a -dimensional (d=2) regular lattice improved by adding long-range shortcuts with probability P (rij)~rij-a, where rij is the lattice distance between sites i and j, and a is a variable exponent. Bias is represented as a probability of the packet to travel at every hop toward the node which has the smallest Manhattan distance to the target node. We study the mean first passage time (MFPT) for different exponent and the scaling of the MFPT with the size of the network . We find that there exists a threshold probability pth ≈0.5 , for p≥pth the optimal transportation condition is obtained with an optimal transport exponent α= d, while for 0pth , and increases with L less than a power law and get close to logarithmical law for 0
Loading...
Availability at HKSYU Library
