Efficient search by optimized intermittent random walks

We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest neighbor site with probability α or go off lattice with probability 1−α to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering α and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability PN that the target remains undetected up to the maximal search time N. We show that even in this simple model, a number of very efficient search strategies can lead to a decrease of PN by orders of magnitude upon appropriate choices of α and L. We demonstrate that, in general, such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions. In addition, such intermittent strategies appear to be more advantageous than Lévy-based ones in that they lead to more thorough exploration of visited regions in space and thus lend themselves to parallelization of the search processes. PACS numbers: 05.40.−a, 87.23.−n 1751-8113/09/434008+14$30.00 © 2009 IOP Publishing Ltd Printed in the UK 1 J. Phys. A: Math. Theor. 42 (2009) 434008 G Oshanin et al