  The central problem in computational algebraic topology is the computation of
the homotopy groups of a given space, represented as a simplicial set.
Algorithms have been found which achieve this, but the running times depend on
the size of the input simplicial set. In order to reduce this dependence on the
simplicial set chosen, we describe in this paper a procedure which, given a
prime $p$ and a finite, simply-connected simplicial set with finite integral
homology, finds a $p$-locally equivalent simplicial set with size upper bounded
by a function of dimension and homology. Using this in conjunction with the
above algorithm, the $p$-local homology can be calculated such that the running
time dependence on the size of the initial simplicial set is contained in a
separate preprocessing step.
