Before revision:  Specifically , 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 O(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.
After revision:  Specifically , 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 O(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.