Efficient data structure for representing and simplifying simplicial complexes in high dimensions

@inproceedings{Attali2011EfficientDS,
  title={Efficient data structure for representing and simplifying simplicial complexes in high dimensions},
  author={Dominique Attali and Andr{\'e} Lieutier and David Salinas},
  booktitle={Symposium on Computational Geometry},
  year={2011}
}
We study the simplification of simplicial complexes by repeated edge contractions. First, we extend to arbitrary simplicial complexes the statement that edges satisfying the link condition can be contracted while preserving the homotopy type. Our primary interest is to simplify flag complexes such as Rips complexes for which it was proved recently that they can provide topologically correct reconstructions of shapes. Flag complexes (sometimes called clique complexes) enjoy the nice property of… CONTINUE READING
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