Loops in reeb graphs of 2-manifolds | Zendy

Kree Cole-McLaughlin | Zendy; Herbert Edelsbrunner | Zendy; John Harer | Zendy; Vijay Natarajan | Zendy; Valerio Pascucci | Zendy

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Loops in reeb graphs of 2-manifolds

Author(s) -

Kree Cole-McLaughlin,

Herbert Edelsbrunner,

John Harer,

Vijay Natarajan,

Valerio Pascucci

Publication year - 2003

Publication title -

osti oai (u.s. department of energy office of scientific and technical information)

Language(s) - English

Resource type - Conference proceedings

DOI - 10.1145/777792.777844

Subject(s) - mathematics , combinatorics , graph , morse code , manifold (fluid mechanics) , boundary (topology) , computer science , mathematical analysis , mechanical engineering , telecommunications , engineering

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(nlogn), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

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