  The known linear-time kernelizations for $d$-Hitting Set guarantee linear
worst-case running times using a quadratic-size data structure (that is not
fully initialized). Getting rid of this data structure, we show that problem
kernels of asymptotically optimal size $O(k^d)$ for $d$-Hitting Set are
computable in linear time and space. Additionally, we experimentally compare
the linear-time kernelizations for $d$-Hitting Set to each other and to a
classical data reduction algorithm due to Weihe.
