Before revision: We improve two linear-time data reduction algorithms for the d-Hitting Set problem to work in linear space, thus obtaining the first algorithms for computing problem kernels of asymptotically optimal size O(k^d) for d-Hitting Set  in linear time and space.
After revision: We improve two linear-time kernelizations for d-Hitting Set problem to work in linear space, thus obtaining the first algorithms for computing problem kernels of asymptotically optimal size O(k^d) for d-Hitting Set in linear time and space.