PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Zigzag persistent homology in matrix multiplication time
Nikola Milosavljević, Dmitriy Morozov and Primož Škraba
In: SCG 2011, 13-15 Jun 2011, Paris, France.

Abstract

We present a new algorithm for computing zigzag persistent homology, an algebraic structure which encodes changes to homology groups of a simplicial complex over a sequence of simplex additions and deletions. Provided that there is an algorithm that multiplies two n n matrices in M(n) time, our algorithm runs in O(M(n) + n2 log2 n) time for a sequence of n additions and deletions. In particular, the running time is O(n2:376), by result of Coppersmith and Winograd. The fastest previously known algorithm for this problem takes O(n3) time in the worst case.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8737
Deposited By:Jan Rupnik
Deposited On:21 February 2012