Computing Multidimensional Persistence
arXiv:0907.2423
Abstract
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.
This paper has been withdrawn by the authors. Journal of Computational Geometry, 1(1) 2010, pages 72-100. http://jocg.org/index.php/jocg/article/view/19
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