  We simulate crystallization and melting with local Monte Carlo (LMC),
event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD)
in systems with up to one million three-dimensional hard spheres. We illustrate
that our implementations of the three algorithms rigorously coincide in their
equilibrium properties. We then study nucleation in the NVE ensemble from the
fcc crystal into the homogeneous liquid phase and from the liquid into the
homogeneous crystal. ECMC and EDMD both approach equilibrium orders of
magnitude faster than LMC. ECMC is also notably faster than EDMD, especially
for the equilibration into a crystal from a disordered initial condition at
high density. ECMC can be trivially implemented for hard-sphere and for
soft-sphere potentials, and we suggest possible applications of this algorithm
for studying jamming and the physics of glasses, as well as disordered systems.
