If You Must Choose Among Your Children, Pick the Right One
Benjamin Holmgren, Bradley McCoy, Brittany Fasy, and David Millman

TL;DR
This paper analyzes algorithms for extending vertex functions to discrete Morse functions on simplicial complexes, offering a more efficient description suitable for high-dimensional data.
Contribution
It provides a new, faster description of an existing algorithm for discrete Morse function extension using the directed Hasse diagram.
Findings
Faster runtime for high-dimensional data
No increase in space complexity
Improved understanding of the algorithm's structure
Abstract
Given a simplicial complex and an injective function from the vertices of to , we consider algorithms that extend to a discrete Morse function on . We show that an algorithm of King, Knudson and Mramor can be described on the directed Hasse diagram of . Our description has a faster runtime for high dimensional data with no increase in space.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Genomics and Chromatin Dynamics
