  The theory of multidimensional persistence captures the topology of a
multifiltration -- a multiparameter family of increasing spaces.
Multifiltrations arise naturally in the topological analysis of scientific
data. In this paper, we give a polynomial time algorithm for computing
multidimensional persistence. We recast this computation as a problem within
computational algebraic geometry and utilize algorithms from this area to solve
it. While the resulting problem is Expspace-complete and the standard
algorithms take doubly-exponential time, we exploit the structure inherent
withing multifiltrations to yield practical algorithms. We implement all
algorithms in the paper and provide statistical experiments to demonstrate
their feasibility.
