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COMPGEOM
2011
ACM

Zigzag persistent homology in matrix multiplication time

9 years 1 months ago
Zigzag persistent homology in matrix multiplication time
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. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; G.2.1 [Discrete Mathematics]: Combinatorics General Terms Algorithms, Theory Keywords Zigzag persistent homology, matrix multiplication.
Nikola Milosavljevic, Dmitriy Morozov, Primoz Skra
Added 25 Aug 2011
Updated 25 Aug 2011
Type Journal
Year 2011
Where COMPGEOM
Authors Nikola Milosavljevic, Dmitriy Morozov, Primoz Skraba
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