  New algorithms useful for the calculation of dynamic aperture and momentum
acceptance in circular accelerators are developed and presented. The flood-fill
tool from raster graphics inspired us to efficiently compute dynamic apertures
by minimizing required trackings on stable initial coordinates, leading to
several factors of speed-up with respect to standard algorithms. A novel
technique for momentum acceptance calculations, Fast Touschek Tracking, is
developed. Thorough benchmarking using modern accelerator codes shows that the
new technique can provide one or two orders of magnitude faster computation of
local momentum acceptances with only limited loss of accuracy.
