Geodesic-preserving polygon simplification

Oswin Aichholzer, Thomas Hackl, Matias Korman, Alexander Pilz, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon P by a polygon P′ such that (1) P′, contains P, (2) P′, has its reflex vertices at the same positions as P, and (3) the number of vertices of P′ is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both P and P′, our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of P.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
Number of pages11
Publication statusPublished - 2013
Externally publishedYes
Event24th International Symposium on Algorithms and Computation, ISAAC 2013 - Hong Kong, China
Duration: 2013 Dec 162013 Dec 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8283 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other24th International Symposium on Algorithms and Computation, ISAAC 2013
CityHong Kong

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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