Fat triangles determine linearly many holes

Jiri Matousek; Nathaly Miller; Janos Pach; Micha Sharir; Shmuel Sifrony; Emo Welzl

Fat triangles determine linearly many holes

Jiri Matousek^*, Nathaly Miller, Janos Pach, Micha Sharir, Shmuel Sifrony, Emo Welzl

^*Corresponding author for this work

Charles University

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

33 Scopus citations

Abstract

It is shown that for every fixed δ > 0 the following holds: if F is a union of n triangles, all of whose angles are at least δ, then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2^α(n) log n) is given. Several applications of these results are presented.

Original language	English
Title of host publication	Annual Symposium on Foundations of Computer Science (Proceedings)
Publisher	Publ by IEEE
Pages	49-58
Number of pages	10
ISBN (Print)	0818624450
State	Published - Dec 1991
Externally published	Yes
Event	Proceedings of the 32nd Annual Symposium on Foundations of Computer Science - San Juan, PR, USA Duration: 1 Oct 1991 → 4 Oct 1991

Publication series

Name	Annual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)	0272-5428

Conference

Conference	Proceedings of the 32nd Annual Symposium on Foundations of Computer Science
City	San Juan, PR, USA
Period	1/10/91 → 4/10/91

Cite this

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title = "Fat triangles determine linearly many holes",

abstract = "It is shown that for every fixed δ > 0 the following holds: if F is a union of n triangles, all of whose angles are at least δ, then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2α(n) log n) is given. Several applications of these results are presented.",

author = "Jiri Matousek and Nathaly Miller and Janos Pach and Micha Sharir and Shmuel Sifrony and Emo Welzl",

year = "1991",

month = dec,

language = "אנגלית",

isbn = "0818624450",

series = "Annual Symposium on Foundations of Computer Science (Proceedings)",

publisher = "Publ by IEEE",

pages = "49--58",

booktitle = "Annual Symposium on Foundations of Computer Science (Proceedings)",

note = "Proceedings of the 32nd Annual Symposium on Foundations of Computer Science ; Conference date: 01-10-1991 Through 04-10-1991",

}

Matousek, J, Miller, N, Pach, J, Sharir, M, Sifrony, S & Welzl, E 1991, Fat triangles determine linearly many holes. in Annual Symposium on Foundations of Computer Science (Proceedings). Annual Symposium on Foundations of Computer Science (Proceedings), Publ by IEEE, pp. 49-58, Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, San Juan, PR, USA, 1/10/91.

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T1 - Fat triangles determine linearly many holes

AU - Matousek, Jiri

AU - Miller, Nathaly

AU - Pach, Janos

AU - Sharir, Micha

AU - Sifrony, Shmuel

AU - Welzl, Emo

PY - 1991/12

Y1 - 1991/12

N2 - It is shown that for every fixed δ > 0 the following holds: if F is a union of n triangles, all of whose angles are at least δ, then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2α(n) log n) is given. Several applications of these results are presented.

AB - It is shown that for every fixed δ > 0 the following holds: if F is a union of n triangles, all of whose angles are at least δ, then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2α(n) log n) is given. Several applications of these results are presented.

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T3 - Annual Symposium on Foundations of Computer Science (Proceedings)

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BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - Publ by IEEE

T2 - Proceedings of the 32nd Annual Symposium on Foundations of Computer Science

Y2 - 1 October 1991 through 4 October 1991

ER -

Fat triangles determine linearly many holes

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