  Using molecular dynamics simulations, we study the slow dynamics of
supercooled liquids confined in a random matrix of immobile obstacles. We study
the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms
of the density correlation function, the mean square displacement, the
nonlinear dynamic susceptibility, the non-Gaussian parameter, and the
fragility. Cooperative and spatially heterogeneous dynamics are suppressed as
the obstacle density increases, which lead to the more Arrhenius-like behavior
in the temperature dependence of the relaxation time. Our findings are
qualitatively consistent with the results of recent experimental and numerical
studies for various classes of spatially heterogeneous systems. We also
investigate the dependence of the dynamics of mobile particles on the protocol
to generate the random matrix. A reentrant transition from the arrested phase
to the liquid phase as the mobile particle density {\it increases} is observed
for a class of protocols. This reentrance is explained in terms of the
distribution of the volume of the voids that are available to the mobile
particles.
