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DOI 10.34229/KCA2522-9664.25.6.5
UDC 004.021+004.043+004.051

V. Tereshchenko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
vtereshch@gmail.com

A. Prishlyak
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
prishlyak@knu.ua

M. Osiponok
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
osipyonok@ukr.net


THE CONSTRUCTION OF EFFICIENT ALGORITHMS FOR ADDRESSING
CERTAIN COMPUTATIONAL GEOMETRY PROBLEMS
USING REEB GRAPHS

Abstract. The paper studies the properties of the Reeb graph and the algorithm for its construction, which is based on the sweep line technique. The research aims to evaluate the potential of using the Reeb graph to create efficient algorithms for solving certain problems of computational geometry. In this study, we developed an algorithm that decomposes a planar polygon into a set of monotone polygons while simultaneously triangulating them based on the properties of the Reeb graph. Additionally, we analyze the efficiency of this algorithm in comparison to other triangulation methods.

Keywords: computational geometry, model of a unified algorithmic environment, planar polygon, Reeb graph, triangulation.


full text

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