  We present a new efficient method for Monte Carlo simulations of
diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett.,
97:230602, 2006], the new algorithm skips the traditional small diffusion hops
and propagates the diffusing particles over long distances through a sequence
of super-hops, one particle at a time. By partitioning the simulation space
into non-overlapping protecting domains each containing only one or two
particles, the algorithm factorizes the N-body problem of collisions among
multiple Brownian particles into a set of much simpler single-body and two-body
problems. Efficient propagation of particles inside their protective domains is
enabled through the use of time-dependent Green's functions (propagators)
obtained as solutions for the first-passage statistics of random walks. The
resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian
particle propagates inside its own protective domain and on its own time clock.
The algorithm reproduces the statistics of the underlying Monte-Carlo model
exactly. Extensive numerical examples demonstrate that for an important class
of diffusion-reaction models the new algorithm is efficient at low particle
densities, where other existing algorithms slow down severely.
