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cubical complex from top_cells: useless boundary cells

Open mglisse opened this issue 1 year ago • 0 comments

In a cubical complex like this image whose filtration is computed from the top-dimensional cells, we do not need to consider all the cells to compute persistent homology. We can remove the first 2 rows (0-17), the last 2 rows (27-44), the first 2 columns (0,1,9,10,18,19,27,28,36,37) and the last 2 columns (7,8,16,...). Indeed, the first 2 columns have the same filtration values, which are at least as large as the 3rd column, and we can simply collapse the pairs (9,10), (27,28), (0,1), (18,19), etc. In this small example, it would leave us with just the cells 20-24 (of course the gain is much smaller with more realistic sizes). Supposedly, taking advantage of this should make the top_cells version slightly faster than the vertices version.

mglisse avatar Mar 02 '23 07:03 mglisse