Before revision:  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:  We prove that in a finite two-dimensional torus, an intermittent L\'evy walk whose step-lengths are distributed according to an ]. Despite numerous attempts, there is currently no conclusive analytical evidence that L\'evy flights are preferable strategies in higher dimensions than one. Here we show that the optimality of inverse-square power-law is a near-optimal strategy for finding ] sparse targets of any size and shape.