Before revision:  That is, in a square torus of area~n, and assuming that the detection radius is normalized to 1, the strategy finds any connected set of diameter D in (n/D) expected time, whereas \Omega(n/D) is an unconditional lower bound on the expected time, that holds even when assuming that the shape and size of the target are known. Furthermore, this particular L\'evy process stands in stark contrast to many other basic intermittent processes, including all other L\'evy walks, whose competitive ratio is shown to be polynomial in n, for wide ranges of target scales .
After revision:  That is, in a square torus of area~n, and assuming that the detection radius is normalized to 1, the strategy finds any connected set of diameter D in Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent L\'evy process stands in stark contrast to many other basic intermittent processes, including all other L\'evy walks, whose competitive ratio is shown to be polynomial in n, for wide ranges of target scales .