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Zigzag persistent homology in matrix multiplication time
Nikola Milosavljević, Dmitriy Morozov and Primož Škraba
In: SCG 2011, 13-15 Jun 2011, Paris, France.
AbstractWe 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) |
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| Project Keyword: | Project Keyword UNSPECIFIED |
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| Subjects: | Theory & Algorithms |
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| ID Code: | 8737 |
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| Deposited By: | Jan Rupnik |
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| Deposited On: | 21 February 2012 |
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