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Register a new userEfficient search by optimized intermittent random walks
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Gleb Oshanin
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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 alpha, or go off lattice with probability 1 - alpha to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering alpha and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability P_N 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 P_N by orders of magnitude upon appropriate choices of alpha 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 Levy-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.
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This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.
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