Random discrete morse theory and a new library of triangulations

Bruno Benedetti, Frank H. Lutz

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We introduce random discrete Morse theory as a computational scheme to measure the complexity of a triangulation. The idea is to try to quantify the frequency of discrete Morse matchings with few critical cells. Our measure will depend on the topology of the space, but also on how nicely the space is triangulated. The scheme we propose looks for optimal discrete Morse functions with an elementary random heuristic. Despite its naiveté, this approach turns out to be very successful even in the case of huge inputs. In our view, the existing libraries of examples in computational topology are "too easy" for testing algorithms based on discrete Morse theory. We propose a new library containing more complicated (and thus more meaningful) test examples.

Original languageEnglish (US)
Pages (from-to)66-94
Number of pages29
JournalExperimental Mathematics
Volume23
Issue number1
DOIs
StatePublished - Jan 2 2014
Externally publishedYes

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Keywords

  • Collapsibility
  • Knots in triangulations
  • Library of triangulations
  • Random discrete Morse theory
  • Shellability

ASJC Scopus subject areas

  • Mathematics(all)

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