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cs.CG2026
Discrete homology computations by reduction to zero differentials
Sterling Ebel, Chris Kapulkin, Nathan Kershaw
We develop a new algorithm for computing (persistent) discrete homology of graphs using reduction to zero differentials and active enumeration. This allows us to compute the fourth…
cs.CG2026
RedZeD: Computing persistent homology by Reduction to Zero Differentials
Chris Kapulkin, Nathan Kershaw
We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the exist…
cs.CG2024
Faster computations of discrete homology
Chris Kapulkin, Nathan Kershaw
Machine computation of the discrete homology of graphs has stopped at degree two. We present an algorithm that reaches degree four. It generates the singular cubes inductively, pai…