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Nov 21, 2012 at 0:08 comment added Russ Woodroofe Benedetti and Lutz have done some experimental work with algorithmically generating discrete Morse collapsing schemes. An announcement of this work can be found at math.kth.se/~brunoben/OWR2012_Benedetti.pdf although as far as I can tell the full paper hasn't yet made it to the arXiv.
Jan 21, 2012 at 10:21 comment added Liviu Nicolaescu The function that associates to each cell its dimension is a combinatorial Morse function. Granted, it is not the most efficient computationally.
Jan 20, 2012 at 21:49 history answered Vidit Nanda CC BY-SA 3.0