Optimization of random searches on regular lattices.

Area of Science:

• Statistical Physics
• Computational Science
• Network Theory

Background:

• Random walks are fundamental models for diffusion and search processes.
• Understanding search efficiency in complex environments is crucial for various applications.
• Previous studies often focused on continuous spaces or simpler lattice structures.

Purpose of the Study:

• To evaluate the efficiency of random search strategies on discrete lattices.
• To investigate the impact of lattice topology and boundary conditions on search performance.
• To determine optimal search parameters for different search environments (destructive vs. nondestructive).

Main Methods:

• Simulating random searches on square and triangular lattices with periodic boundary conditions.
• Employing power-law distributed step lengths for the search strategy.
• Analyzing search efficiency based on the number of steps required to find targets.

Main Results:

• Search efficiency is sensitive to lattice topology and periodic boundary conditions.
• Optimal power-law exponents vary with target site density.
• Destructive search environments exhibit different optimal strategies compared to nondestructive ones.
• Discrete lattice search results show deviations from continuous space models.

Conclusions:

• Lattice structure and boundary conditions significantly influence random search efficiency.
• Power-law step length distributions offer tunable search strategies adaptable to varying conditions.
• The distinction between destructive and nondestructive searches is critical for optimizing search protocols.