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Open AccessArticle

An Efficient Data Retrieval Parallel Reeb Graph Algorithm

by Mustafa Hajij 1,* and Paul Rosen 2
1
Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053, USA
2
Department of Computer Science and Engineering, University of South Florida, Tampa, FL 33620, USA
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(10), 258; https://doi.org/10.3390/a13100258
Received: 15 August 2020 / Revised: 22 September 2020 / Accepted: 22 September 2020 / Published: 12 October 2020
(This article belongs to the Special Issue Topological Data Analysis)
The Reeb graph of a scalar function that is defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence, the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms. View Full-Text
Keywords: topological data analysis; parallel algorithms; reeb graph topological data analysis; parallel algorithms; reeb graph
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Hajij, M.; Rosen, P. An Efficient Data Retrieval Parallel Reeb Graph Algorithm. Algorithms 2020, 13, 258.

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