On the boundary complexity of the union of fat triangles

Janos Pach, G. Tardos

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

5 Citations (Scopus)

Abstract

A triangle is said to be δ-fat if its smallest angle is at least δ>0. A connected component of the complement of the union of a family of triangles is called hole. It is shown that any family of δ-fat triangles in the plane determines at most O (n/δ log 2/δ) holes. This improves on some earlier bounds of Efrat, Rote, Sharir, Matousek et al. Solving a problem of Agarwal and Bern, we also give a general upper bound for the number of holes determined by n triangles in the plane with given angles. As a corollary, we obtain improved upper bounds for the boundary complexity of the union of fat polygons in the plane, which, in turn, leads to better upper bounds for the running times of some known algorithms for motion planning, for finding a separator line for a set of segments, etc.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science - Proceedings
PublisherIEEE
Pages423-431
Number of pages9
Publication statusPublished - 2000
Event41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA
Duration: Nov 12 2000Nov 14 2000

Other

Other41st Annual Symposium on Foundations of Computer Science (FOCS 2000)
CityRedondo Beach, CA, USA
Period11/12/0011/14/00

Fingerprint

Oils and fats
Motion planning
Separators

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Pach, J., & Tardos, G. (2000). On the boundary complexity of the union of fat triangles. In Annual Symposium on Foundations of Computer Science - Proceedings (pp. 423-431). IEEE.

On the boundary complexity of the union of fat triangles. / Pach, Janos; Tardos, G.

Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, 2000. p. 423-431.

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

Pach, J & Tardos, G 2000, On the boundary complexity of the union of fat triangles. in Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, pp. 423-431, 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), Redondo Beach, CA, USA, 11/12/00.
Pach J, Tardos G. On the boundary complexity of the union of fat triangles. In Annual Symposium on Foundations of Computer Science - Proceedings. IEEE. 2000. p. 423-431
Pach, Janos ; Tardos, G. / On the boundary complexity of the union of fat triangles. Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, 2000. pp. 423-431
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