  The partial Hamiltonian analysis of the Ho\v{r}ava-type action presented in
the paper by M. Chaichian, S. Nojiri, S. D. Odintsov, M. Oksanen, A. Tureanu
(Class. Quant. Grav. 27 (2011) 185021) is incorrect; for the authors' choice of
variables, a covariant shift, instead of a contravariant shift which is the one
usually used in General Relativity (GR) in ADM variables, the true algebra of
constraints differs from what they presented. The algebra of constraints for
their choice of variables is explicitly given for GR and compared with the
standard algebra.
