Cover times with stochastic resetting.

Area of Science:

• Physics
• Mathematics
• Computer Science

Background:

• Cover times measure the speed of exhaustive search processes.
• Stochastic search processes are fundamental in fields like physics and computer science.
• Stochastic resetting is a technique to accelerate search by periodically restarting the process.

Purpose of the Study:

• To approximate moments of cover times for diverse stochastic search processes.
• To analyze the impact of stochastic resetting on search efficiency in continuous and discrete systems.
• To derive conditions under which stochastic resetting enhances search speed.

Main Methods:

• Approximation of moments for cover times in d-dimensional continuous space and discrete networks.
• Analysis of various search processes: diffusion, run-and-tumble particles, and Markov jump processes.
• Investigation of different stochastic resetting time distributions.

Main Results:

• Accurate approximations for cover time moments across various search processes and resetting distributions.
• Demonstration of exponentially fast error decay for diffusive search approximations.
• Derivation of a criterion for when minimal stochastic resetting reduces mean cover time.

Conclusions:

• The developed approximations are broadly applicable to many stochastic search scenarios.
• Stochastic resetting can be a powerful tool to optimize search efficiency.
• A clear criterion is established for the beneficial application of stochastic resetting in discrete search processes.