Random walks with both resetting and nonnearest-neighbor jumps

In this study, we propose a novel random walk strategy, termed “Random Walks with both Resetting and Nonnearest-Neighbor Jumps (RW-RNNJ)”. In order to determine RW-RNNJ’s capability to efficiently search for immobile targets on networks, we focused on the first passage problem and derived exact solutions for mean first passage time (MFPT) and global mean first passage time (GMFPT) on the (2,2) flowers network by the approach of probability generating function. The obtained results show that introduced resetting mechanism significantly reduces GMFPT even for large-scale networks, while nonnearest-neighbor jumps can alter the optimal choice of the resetting probability and have a linear effect on GMFPT. Therefore, the impact of resetting on search efficiency is global, while the effect of nonnearest-neighbor jumps is local. In summary, the findings obtained here may pave the way for optimizing diverse stochastic exploration processes such as animal foraging and the trapping of diffusing molecules in large networked systems.