  Many spin systems affected by critical slowing down can be efficiently
simulated using cluster algorithms. Where such systems have long-range
interactions, suitable formulations can additionally bring down the
computational effort for each update from O($N^2$) to O($N\ln N$) or even
O($N$), thus promising an even more dramatic computational speed-up. Here, we
review the available algorithms and propose a new and particularly efficient
single-cluster variant. The efficiency and dynamical scaling of the available
algorithms are investigated for the Ising model with power-law decaying
interactions.
