Speeding up the incremental construction of the union of geometric objects in practice

Eti Ezra; Dan Halperin; Micha Sharir

doi:10.1007/3-540-45749-6_43

Speeding up the incremental construction of the union of geometric objects in practice

Eti Ezra, Dan Halperin, Micha Sharir

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We present a new incremental algorithm for constructing the union of n triangles in the plane. In our experiments, the new algorithm, which we call the Disjoint-Cover (DC) algorithm, performs significantly better than the standard randomized incremental construction (RIC) of the union. Our algorithm is rather hard to analyze rigorously, but we provide an initial such analysis, which yields an upper bound on its performance that is expressed in terms of the expected cost of the RIC algorithm. Our approach and analysis generalize verbatim to the construction of the union of other objects in the plane, and, with slight modifications, to three dimensions. We present experiments with a software implementation of our algorithm using the Cgal library of geometric algorithms.

Original language	English
Title of host publication	Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings
Editors	Rolf Möhring, Rajeev Raman
Publisher	Springer Verlag
Pages	473-484
Number of pages	12
ISBN (Electronic)	3540441808, 9783540441809
DOIs	https://doi.org/10.1007/3-540-45749-6_43
State	Published - 2002
Externally published	Yes
Event	10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy Duration: 17 Sep 2002 → 21 Sep 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2461
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th Annual European Symposium on Algorithms, ESA 2002
Country/Territory	Italy
City	Rome
Period	17/09/02 → 21/09/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Funding

✩ Work reported in this paper has been supported in part by the IST Programme of the EU as Shared-cost RTD (FET Open) Projects under Contract No IST-2000-26473 (ECG—Effective Computational Geometry for Curves and Surfaces) and No IST-2001-39250 (MOVIE—Motion Planning in Virtual Environments), by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), and by the Hermann Minkowski– Minerva Center for Geometry at Tel Aviv University. Micha Sharir has also been supported by NSF Grants CCR-97-32101 and CCR-00-98246, and by a grant from the US–Israeli Binational Science Foundation. * Corresponding author.

Funders	Funder number
US–Israeli Binational Science Foundation
National Science Foundation	CCR-00-98246, CCR-97-32101
Israel Academy of Sciences and Humanities
Israel Science Foundation
Tel Aviv University

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10.1007/3-540-45749-6_43

Cite this

Ezra, E., Halperin, D., & Sharir, M. (2002). Speeding up the incremental construction of the union of geometric objects in practice. In R. Möhring, & R. Raman (Eds.), Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings (pp. 473-484). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2461). Springer Verlag. https://doi.org/10.1007/3-540-45749-6_43

Ezra, Eti ; Halperin, Dan ; Sharir, Micha. / Speeding up the incremental construction of the union of geometric objects in practice. Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings. editor / Rolf Möhring ; Rajeev Raman. Springer Verlag, 2002. pp. 473-484 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Ezra, E, Halperin, D & Sharir, M 2002, Speeding up the incremental construction of the union of geometric objects in practice. in R Möhring & R Raman (eds), Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2461, Springer Verlag, pp. 473-484, 10th Annual European Symposium on Algorithms, ESA 2002, Rome, Italy, 17/09/02. https://doi.org/10.1007/3-540-45749-6_43

Speeding up the incremental construction of the union of geometric objects in practice. / Ezra, Eti; Halperin, Dan; Sharir, Micha.
Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings. ed. / Rolf Möhring; Rajeev Raman. Springer Verlag, 2002. p. 473-484 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2461).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ezra E, Halperin D, Sharir M. Speeding up the incremental construction of the union of geometric objects in practice. In Möhring R, Raman R, editors, Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings. Springer Verlag. 2002. p. 473-484. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45749-6_43

Speeding up the incremental construction of the union of geometric objects in practice

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