Persistent Homology and Nested Dissection

@inproceedings{Kerber2016PersistentHA,
  title={Persistent Homology and Nested Dissection},
  author={Michael Kerber and Don Sheehy and P. Skraba},
  booktitle={SODA},
  year={2016}
}
Nested dissection exploits the underlying topology to do matrix reductions while persistent homology exploits matrix reductions to the reveal underlying topology. It seems natural that one should be able to combine these techniques to beat the currently best bound of matrix multiplication time for computing persistent homology. However, nested dissection works by fixing a reduction order, whereas persistent homology generally constrains the ordering according to an input filtration. Despite… Expand
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References

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Matrix sparsification and nested dissection over arbitrary fields
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