Notes on the Distributed Computation of Merge Trees on CW-Complexes

Landge, Aaditya G.; Bremer, Peer Timo; Gyulassy, Attila; Pascucci, Valerio

doi:10.1007/978-3-319-44684-4_20

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2020

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“…Persistence has been used to study statistical mechanics [20], hypothesis testing [6], image analysis [7], complex networks [19], and many other phenomena. Recently, there has been interest in studying merge trees, a special kind of persistence [15,17]. Part of the advantage of studying a merge tree instead of the persistence diagram is that the merge tree gives more detailed information about precisely which components merged with which other components.…”

Section: Introductionmentioning

confidence: 99%

Merge trees in discrete Morse theory

Johnson¹,

Scoville²

2020

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In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse functions based on the induced merge tree. We then relate the matching number of a tree to a certain invariant of the induced merge tree. Finally, we count the number of merge trees that can be induced on a star graph and characterize the induced merge tree.

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