  We review the problem of finding an apparent horizon in Cauchy data (Sigma,
g_ab, K_ab) in three space dimensions without symmetries. We describe a family
of algorithms which includes the pseudo-spectral apparent horizon finder of
Nakamura et al. and the curvature flow method proposed by Tod as special cases.
We suggest that other algorithms in the family may combine the speed of the
former with the robustness of the latter. A numerical implementation for Cauchy
data given on a grid in Cartesian coordinates is described, and tested on
Brill-Lindquist and Kerr initial data. The new algorithm appears faster and
more robust than previous ones.
