Before revision: We address the general question of what is the best strategy to employ when searching for targets of unpredictable sizes. Motivated by biological scenarios, we focus on generalized random walk strategies, in which step-lengths follow a given distribution, while their direction is randomly uniform. To capture common biological scenarios in which motion degrades detection, we further restrict attention to intermittent settings, which means that the searcher can detect a target only while being "immobile", that is , in-between moving steps. We prove that in a finite two-dimensional torus, an intermittent L\'evy walk whose step-lengths are distributed according to an ] inverse-square power-law is a near-optimal strategy for finding ] sparse targets of any size and shape.
After revision:  L\'evy walk whose step-lengths are distributed according to an ] inverse-square power-law is a near-optimal strategy for finding ] sparse targets of any size and shape.