Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7375672 | Physica A: Statistical Mechanics and its Applications | 2018 | 16 Pages |
Abstract
Search is a universal behavior related to many types of intelligent individuals. While most studies have focused on search in two or infinite-dimensional space, it is still missing how search can be optimized in three-dimensional space. Here we study random searches on three-dimensional (3d) square lattices with periodic boundary conditions, and explore the optimal search strategy with a power-law step length distribution, p(l)â¼lâμ, known as Lévy flights. We find that compared to random searches on two-dimensional (2d) lattices, the optimal exponent μopt on 3d lattices is relatively smaller in non-destructive case and remains similar in destructive case. We also find μopt decreases as the lattice length in z direction increases under high target density. Our findings may help us to understand the role of spatial dimension in search behaviors.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Benhao Yang, Shunkun Yang, Jiaquan Zhang, Daqing Li,