  The computational cost of searching for new pulsars is a limiting factor for
upcoming radio telescopes such as SKA. We introduce four new algorithms: an
optimal constant-period search, a coherent tree search which permits optimal
searching with O(1) cost per model, a semicoherent search which combines
information from coherent subsearches while preserving as much phase
information as possible, and a hierarchical search which interpolates between
the coherent and semicoherent limits. Taken together, these algorithms improve
the computational cost of pulsar search by several orders of magnitude. In this
paper, we consider the simple case of a constant-acceleration phase model, but
our methods should generalize to more complex search spaces.
