---
_id: '4060'
abstract:
- lang: eng
text: This paper offers combinatorial results on extremum problems concerning the
number of tetrahedra in a tetrahedrization of n points in general position in
three dimensions, i.e. such that no four points are co-planar, It also presents
an algorithm that in O(n log n) time constructs a tetrahedrization of a set of
n points consisting of at most 3n-11 tetrahedra.
acknowledgement: Research of the first author is supported by Amoco Fnd. Fac. Dec.
Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902,
and research of the third author is supported in part by ONR Grant N00014-85K0570
and by NSF Grant DMS 8504322.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Franco
full_name: Preparata, Franco
last_name: Preparata
- first_name: Douglas
full_name: West, Douglas
last_name: West
citation:
ama: Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions.
Journal of Symbolic Computation. 1990;10(3-4):335-347. doi:10.1016/S0747-7171(08)80068-5
apa: Edelsbrunner, H., Preparata, F., & West, D. (1990). Tetrahedrizing point
sets in three dimensions. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(08)80068-5
chicago: Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing
Point Sets in Three Dimensions.” Journal of Symbolic Computation. Elsevier,
1990. https://doi.org/10.1016/S0747-7171(08)80068-5.
ieee: H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in
three dimensions,” Journal of Symbolic Computation, vol. 10, no. 3–4. Elsevier,
pp. 335–347, 1990.
ista: Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three
dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.
mla: Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.”
Journal of Symbolic Computation, vol. 10, no. 3–4, Elsevier, 1990, pp.
335–47, doi:10.1016/S0747-7171(08)80068-5.
short: H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10
(1990) 335–347.
date_created: 2018-12-11T12:06:42Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-23T10:10:35Z
day: '01'
doi: 10.1016/S0747-7171(08)80068-5
extern: '1'
intvolume: ' 10'
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub
month: '01'
oa: 1
oa_version: Published Version
page: 335 - 347
publication: Journal of Symbolic Computation
publication_identifier:
eissn:
- 1095-855X
issn:
- 0747-7171
publication_status: published
publisher: Elsevier
publist_id: '2061'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tetrahedrizing point sets in three dimensions
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 10
year: '1990'
...
---
_id: '4063'
abstract:
- lang: eng
text: This paper describes a general-purpose programming technique, called Simulation
of Simplicity, that can be used to cope with degenerate input data for geometric
algorithms. It relieves the programmer from the task of providing a consistent
treatment for every single special case that can occur. The programs that use
the technique tend to be considerably smaller and more robust than those that
do not use it. We believe that this technique will become a standard tool in writing
geometric software.
acknowledgement: 'Research of both authors was supported by Amoco Foundation Faculty
Development grant CS 1-6-44862. It was partially carried out while both authors
were with the Institutes for Information Processing at the Technical University
of Graz, Austria. The first author also acknowledges support by the National Science
Foundation under grant CCR-8714565. '
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ernst
full_name: Mücke, Ernst
last_name: Mücke
citation:
ama: 'Edelsbrunner H, Mücke E. Simulation of simplicity: A technique to cope with
degenerate cases in geometric algorithms. ACM Transactions on Graphics.
1990;9(1):66-104. doi:10.1145/77635.77639'
apa: 'Edelsbrunner, H., & Mücke, E. (1990). Simulation of simplicity: A technique
to cope with degenerate cases in geometric algorithms. ACM Transactions on
Graphics. ACM. https://doi.org/10.1145/77635.77639'
chicago: 'Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique
to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on
Graphics. ACM, 1990. https://doi.org/10.1145/77635.77639.'
ieee: 'H. Edelsbrunner and E. Mücke, “Simulation of simplicity: A technique to cope
with degenerate cases in geometric algorithms,” ACM Transactions on Graphics,
vol. 9, no. 1. ACM, pp. 66–104, 1990.'
ista: 'Edelsbrunner H, Mücke E. 1990. Simulation of simplicity: A technique to cope
with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 9(1),
66–104.'
mla: 'Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique
to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on
Graphics, vol. 9, no. 1, ACM, 1990, pp. 66–104, doi:10.1145/77635.77639.'
short: H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104.
date_created: 2018-12-11T12:06:43Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T14:58:39Z
day: '01'
doi: 10.1145/77635.77639
extern: '1'
intvolume: ' 9'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/77635.77639
month: '01'
oa_version: None
page: 66 - 104
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: ACM
publist_id: '2058'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Simulation of simplicity: A technique to cope with degenerate cases in geometric
algorithms'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 9
year: '1990'
...
---
_id: '4064'
abstract:
- lang: eng
text: Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median
of squares regression line is a line y = ax + b for which the median of the squared
residuals is a minimum over all choices of a and b. An algorithm is described
that computes such a line in O(n 2) time and O(n) memory space, thus improving
previous upper bounds on the problem. This algorithm is an application of a general
method built on top of the topological sweep of line arrangements.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Diane
full_name: Souvaine, Diane
last_name: Souvaine
citation:
ama: Edelsbrunner H, Souvaine D. Computing least median of squares regression lines
and guided topological sweep. Journal of the American Statistical Association.
1990;85(409):115-119. doi:10.1080/01621459.1990.10475313
apa: Edelsbrunner, H., & Souvaine, D. (1990). Computing least median of squares
regression lines and guided topological sweep. Journal of the American Statistical
Association. American Statistical Association. https://doi.org/10.1080/01621459.1990.10475313
chicago: Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares
Regression Lines and Guided Topological Sweep.” Journal of the American Statistical
Association. American Statistical Association, 1990. https://doi.org/10.1080/01621459.1990.10475313.
ieee: H. Edelsbrunner and D. Souvaine, “Computing least median of squares regression
lines and guided topological sweep,” Journal of the American Statistical Association,
vol. 85, no. 409. American Statistical Association, pp. 115–119, 1990.
ista: Edelsbrunner H, Souvaine D. 1990. Computing least median of squares regression
lines and guided topological sweep. Journal of the American Statistical Association.
85(409), 115–119.
mla: Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares
Regression Lines and Guided Topological Sweep.” Journal of the American Statistical
Association, vol. 85, no. 409, American Statistical Association, 1990, pp.
115–19, doi:10.1080/01621459.1990.10475313.
short: H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association
85 (1990) 115–119.
date_created: 2018-12-11T12:06:43Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T15:10:54Z
day: '01'
doi: 10.1080/01621459.1990.10475313
extern: '1'
intvolume: ' 85'
issue: '409'
language:
- iso: eng
main_file_link:
- url: https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313
month: '01'
oa_version: None
page: 115 - 119
publication: Journal of the American Statistical Association
publication_identifier:
eissn:
- 1537-274X
issn:
- 0003-1291
publication_status: published
publisher: American Statistical Association
publist_id: '2059'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing least median of squares regression lines and guided topological sweep
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 85
year: '1990'
...
---
_id: '4065'
abstract:
- lang: eng
text: We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the
plane, they may be covered with n non-overlapping convex polygons with a total
of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore,
we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound
on the number of slopes implies a new bound on a recently studied transversal
problem.
acknowledgement: 'The first author acknowledges the support by Amoco Fnd. Fat. Dev.
Comput. Sci. l-6-44862. Work on this paper by the second author was supported by
a Shell Fellowship in Computer Science. The third author as supported by the office
of Naval Research under grant NOOO14-86K-0416. '
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Arch
full_name: Robison, Arch
last_name: Robison
- first_name: Xiao
full_name: Shen, Xiao
last_name: Shen
citation:
ama: Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping
polygons. Discrete Mathematics. 1990;81(2):153-164. doi:10.1016/0012-365X(90)90147-A
apa: Edelsbrunner, H., Robison, A., & Shen, X. (1990). Covering convex sets
with non-overlapping polygons. Discrete Mathematics. Elsevier. https://doi.org/10.1016/0012-365X(90)90147-A
chicago: Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets
with Non-Overlapping Polygons.” Discrete Mathematics. Elsevier, 1990. https://doi.org/10.1016/0012-365X(90)90147-A.
ieee: H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping
polygons,” Discrete Mathematics, vol. 81, no. 2. Elsevier, pp. 153–164,
1990.
ista: Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping
polygons. Discrete Mathematics. 81(2), 153–164.
mla: Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.”
Discrete Mathematics, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:10.1016/0012-365X(90)90147-A.
short: H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.
date_created: 2018-12-11T12:06:44Z
date_published: 1990-04-15T00:00:00Z
date_updated: 2022-02-22T15:45:55Z
day: '15'
doi: 10.1016/0012-365X(90)90147-A
extern: '1'
intvolume: ' 81'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub
month: '04'
oa_version: None
page: 153 - 164
publication: Discrete Mathematics
publication_identifier:
eissn:
- 1872-681X
issn:
- 0012-365X
publication_status: published
publisher: Elsevier
publist_id: '2060'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Covering convex sets with non-overlapping polygons
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 81
year: '1990'
...
---
_id: '4066'
abstract:
- lang: eng
text: 'We consider several problems involving points and planes in three dimensions.
Our main results are: (i) The maximum number of faces boundingm distinct cells
in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells
specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii)
The maximum number of incidences betweenn planes andm vertices of their arrangement
isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for
any>0, for any collection of points no three of which are collinear. (iii)
For an arbitrary collection ofm points, we can calculate the number of incidences
between them andn planes by a randomized algorithm whose expected time complexity
isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any>0. (iv) Givenm points andn
planes, we can find the plane lying immediately below each point in randomized
expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any>0. (v) The maximum
number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an
arrangement ofn hyperplanes ind dimensions,d>3, isO(m 2/3 n d/3 logn+n d–1).
This is also an upper bound for the number of incidences betweenn hyperplanes
ind dimensions andm vertices of their arrangement. The combinatorial bounds in
(i) and (v) and the general bound in (ii) are almost tight.'
acknowledgement: "Supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by
NSF Grant CCR-8714565. Work on this paper by the first author has been supported
by Amoco Fnd. Fac. Dev. Comput. Sci. I-6-44862 and by NSF Grant CCR-87t4565. Work
by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129,
by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment
Corporation, and the IBM Corporation, and by a research grant from the NCRD--the
Israeli National Council for Research and Development. An abstract of this\r\npaper
has appeared in the Proceedings of the 13th International Mathematical Programming
Symposium, Tokyo, 1988, p. 147"
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: Edelsbrunner H, Guibas L, Sharir M. The complexity of many cells in arrangements
of planes and related problems. Discrete & Computational Geometry.
1990;5(1):197-216. doi:10.1007/BF02187785
apa: Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity of many
cells in arrangements of planes and related problems. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/BF02187785
chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity
of Many Cells in Arrangements of Planes and Related Problems.” Discrete &
Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187785.
ieee: H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity of many cells in
arrangements of planes and related problems,” Discrete & Computational
Geometry, vol. 5, no. 1. Springer, pp. 197–216, 1990.
ista: Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity of many cells in
arrangements of planes and related problems. Discrete & Computational Geometry.
5(1), 197–216.
mla: Edelsbrunner, Herbert, et al. “The Complexity of Many Cells in Arrangements
of Planes and Related Problems.” Discrete & Computational Geometry,
vol. 5, no. 1, Springer, 1990, pp. 197–216, doi:10.1007/BF02187785.
short: H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry
5 (1990) 197–216.
date_created: 2018-12-11T12:06:44Z
date_published: 1990-03-01T00:00:00Z
date_updated: 2022-02-22T11:02:41Z
day: '01'
doi: 10.1007/BF02187785
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187785
month: '03'
oa_version: None
page: 197 - 216
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2054'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The complexity of many cells in arrangements of planes and related problems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4067'
abstract:
- lang: eng
text: This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences
between m points and n hyperplanes in four dimensions, assuming all points lie
on one side of each hyperplane and the points and hyperplanes satisfy certain
natural general position conditions. This result has application to various three-dimensional
combinatorial distance problems. For example, it implies the same upper bound
for the number of bichromatic minimum distance pairs in a set of m blue and n
red points in three-dimensional space. This improves the best previous bound for
this problem.
acknowledgement: Research of the first author was supported by the National Science
Foundation under grant CCR-8714565. Work of the second author was supported by Office
of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli
Binational Science Foundation, the NCRD — the Israeli National Council for Research
and Development, and the Fund for Basic Research in Electronics, Computers and Communication
administered by the Israeli Academy of Sciences.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: 'Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications
to counting distances. In: Proceedings of the International Symposium on Algorithms.
Vol 450. Springer; 1990:419-428. doi:10.1007/3-540-52921-7_91'
apa: 'Edelsbrunner, H., & Sharir, M. (1990). A hyperplane Incidence problem
with applications to counting distances. In Proceedings of the International
Symposium on Algorithms (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. https://doi.org/10.1007/3-540-52921-7_91'
chicago: Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem
with Applications to Counting Distances.” In Proceedings of the International
Symposium on Algorithms, 450:419–28. Springer, 1990. https://doi.org/10.1007/3-540-52921-7_91.
ieee: H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications
to counting distances,” in Proceedings of the International Symposium on Algorithms,
Tokyo, Japan, 1990, vol. 450, pp. 419–428.
ista: Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications
to counting distances. Proceedings of the International Symposium on Algorithms.
SIGAL: Special Interest Group on Algorithms, International Symposium on Algorithms
, LNCS, vol. 450, 419–428.
mla: Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with
Applications to Counting Distances.” Proceedings of the International Symposium
on Algorithms, vol. 450, Springer, 1990, pp. 419–28, doi:10.1007/3-540-52921-7_91.
short: H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium
on Algorithms, Springer, 1990, pp. 419–428.
conference:
end_date: 1990-08-18
location: Tokyo, Japan
name: 'SIGAL: Special Interest Group on Algorithms, International Symposium on
Algorithms '
start_date: 1990-08-16
date_created: 2018-12-11T12:06:45Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T14:31:26Z
day: '01'
doi: 10.1007/3-540-52921-7_91
extern: '1'
intvolume: ' 450'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/chapter/10.1007/3-540-52921-7_91
month: '01'
oa_version: None
page: 419 - 428
publication: Proceedings of the International Symposium on Algorithms
publication_identifier:
isbn:
- 978-3-540-52921-7
publication_status: published
publisher: Springer
publist_id: '2056'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A hyperplane Incidence problem with applications to counting distances
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 450
year: '1990'
...
---
_id: '4068'
abstract:
- lang: eng
text: "LetS be a collection ofn convex, closed, and pairwise nonintersecting sets
in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1)
\r\nis called ageometric permutation of S if there is a line that intersects all
sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations.
This upper bound is tight."
acknowledgement: Research of the first author was supported by Amoco Foundation for
Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper
by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381,
National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital
Equipment Corporation and the IBM Corporation.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting
sets in the plane is 2n−2. Discrete & Computational Geometry. 1990;5(1):35-42.
doi:10.1007/BF02187778
apa: Edelsbrunner, H., & Sharir, M. (1990). The maximum number of ways to stabn
convex nonintersecting sets in the plane is 2n−2. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/BF02187778
chicago: Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to
Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational
Geometry. Springer, 1990. https://doi.org/10.1007/BF02187778.
ieee: H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex
nonintersecting sets in the plane is 2n−2,” Discrete & Computational Geometry,
vol. 5, no. 1. Springer, pp. 35–42, 1990.
ista: Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex
nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry.
5(1), 35–42.
mla: Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn
Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational
Geometry, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:10.1007/BF02187778.
short: H. Edelsbrunner, M. Sharir, Discrete & Computational Geometry 5 (1990)
35–42.
date_created: 2018-12-11T12:06:45Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T14:50:34Z
day: '01'
doi: 10.1007/BF02187778
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187778
month: '01'
oa_version: None
page: 35 - 42
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2057'
quality_controlled: '1'
status: public
title: The maximum number of ways to stabn convex nonintersecting sets in the plane
is 2n−2
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4069'
abstract:
- lang: eng
text: Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained
by orthogonal projection of the faces of a convex polytope in d + 1 dimensions.
For example, the Delaunay triangulation of a finite point set is such a cell complex.
This paper shows that the in front/behind relation defined for the faces of C
with respect to any fixed viewpoint x is acyclic. This result has applications
to hidden line/surface removal and other problems in computational geometry.
acknowledgement: Research reported in this paper was supported by the National Science
Foundation under grant CCR-8714565.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. Combinatorica.
1990;10(3):251-260. doi:10.1007/BF02122779
apa: Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension.
Combinatorica. Springer. https://doi.org/10.1007/BF02122779
chicago: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
Combinatorica. Springer, 1990. https://doi.org/10.1007/BF02122779.
ieee: H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,”
Combinatorica, vol. 10, no. 3. Springer, pp. 251–260, 1990.
ista: Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension.
Combinatorica. 10(3), 251–260.
mla: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
Combinatorica, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:10.1007/BF02122779.
short: H. Edelsbrunner, Combinatorica 10 (1990) 251–260.
date_created: 2018-12-11T12:06:45Z
date_published: 1990-09-01T00:00:00Z
date_updated: 2022-02-21T11:08:30Z
day: '01'
doi: 10.1007/BF02122779
extern: '1'
intvolume: ' 10'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02122779
month: '09'
oa_version: None
page: 251 - 260
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer
publist_id: '2050'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An acyclicity theorem for cell complexes in d dimension
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 10
year: '1990'
...
---
_id: '4070'
abstract:
- lang: eng
text: Let S be a set of n closed intervals on the x-axis. A ranking assigns to each
interval, s, a distinct rank, p(s)∊ [1, 2,…,n]. We say that s can see t if p(s)International Journal of Computer Mathematics.
1990;34(3-4):129-144. doi:10.1080/00207169008803871
apa: Edelsbrunner, H., Overmars, M., Welzl, E., Hartman, I., & Feldman, J. (1990).
Ranking intervals under visibility constraints. International Journal of Computer
Mathematics. Taylor & Francis. https://doi.org/10.1080/00207169008803871
chicago: Edelsbrunner, Herbert, Mark Overmars, Emo Welzl, Irith Hartman, and Jack
Feldman. “Ranking Intervals under Visibility Constraints.” International Journal
of Computer Mathematics. Taylor & Francis, 1990. https://doi.org/10.1080/00207169008803871.
ieee: H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, and J. Feldman, “Ranking
intervals under visibility constraints,” International Journal of Computer
Mathematics, vol. 34, no. 3–4. Taylor & Francis, pp. 129–144, 1990.
ista: Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. 1990. Ranking intervals
under visibility constraints. International Journal of Computer Mathematics. 34(3–4),
129–144.
mla: Edelsbrunner, Herbert, et al. “Ranking Intervals under Visibility Constraints.”
International Journal of Computer Mathematics, vol. 34, no. 3–4, Taylor
& Francis, 1990, pp. 129–44, doi:10.1080/00207169008803871.
short: H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International
Journal of Computer Mathematics 34 (1990) 129–144.
date_created: 2018-12-11T12:06:46Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-21T13:19:52Z
day: '01'
doi: 10.1080/00207169008803871
extern: '1'
intvolume: ' 34'
issue: 3-4
language:
- iso: eng
main_file_link:
- url: https://www.tandfonline.com/doi/abs/10.1080/00207169008803871
month: '01'
oa_version: None
page: 129 - 144
publication: International Journal of Computer Mathematics
publication_identifier:
eissn:
- 1029-0265
issn:
- 0020-7160
publication_status: published
publisher: Taylor & Francis
publist_id: '2051'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ranking intervals under visibility constraints
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 34
year: '1990'
...
---
_id: '4071'
abstract:
- lang: eng
text: We show that a triangulation of a set of n points in the plane that minimizes
the maximum angle can be computed in time O(n2 log n) and space O(n). In the same
amount of time and space we can also handle the constrained case where edges are
prescribed. The algorithm iteratively improves an arbitrary initial triangulation
and is fairly easy to implement.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Tiow
full_name: Tan, Tiow
last_name: Tan
- first_name: Roman
full_name: Waupotitsch, Roman
last_name: Waupotitsch
citation:
ama: 'Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2log n) time algorithm for the
MinMax angle triangulation. In: Proceedings of the 6th Annual Symposium on
Computational Geometry. ACM; 1990:44-52. doi:10.1145/98524.98535'
apa: 'Edelsbrunner, H., Tan, T., & Waupotitsch, R. (1990). An O(n^2log n) time
algorithm for the MinMax angle triangulation. In Proceedings of the 6th annual
symposium on Computational geometry (pp. 44–52). Berkley, CA, United States:
ACM. https://doi.org/10.1145/98524.98535'
chicago: Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2log n)
Time Algorithm for the MinMax Angle Triangulation.” In Proceedings of the 6th
Annual Symposium on Computational Geometry, 44–52. ACM, 1990. https://doi.org/10.1145/98524.98535.
ieee: H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2log n) time algorithm
for the MinMax angle triangulation,” in Proceedings of the 6th annual symposium
on Computational geometry, Berkley, CA, United States, 1990, pp. 44–52.
ista: 'Edelsbrunner H, Tan T, Waupotitsch R. 1990. An O(n^2log n) time algorithm
for the MinMax angle triangulation. Proceedings of the 6th annual symposium on
Computational geometry. SCG: Symposium on Computational Geometry, 44–52.'
mla: Edelsbrunner, Herbert, et al. “An O(N^2log n) Time Algorithm for the MinMax
Angle Triangulation.” Proceedings of the 6th Annual Symposium on Computational
Geometry, ACM, 1990, pp. 44–52, doi:10.1145/98524.98535.
short: H. Edelsbrunner, T. Tan, R. Waupotitsch, in:, Proceedings of the 6th Annual
Symposium on Computational Geometry, ACM, 1990, pp. 44–52.
conference:
end_date: 1990-06-09
location: Berkley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:46Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T08:56:42Z
day: '01'
doi: 10.1145/98524.98535
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98535
month: '01'
oa_version: None
page: 44 - 52
publication: Proceedings of the 6th annual symposium on Computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2052'
quality_controlled: '1'
status: public
title: An O(n^2log n) time algorithm for the MinMax angle triangulation
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4072'
abstract:
- lang: eng
text: We show that the total number of edges ofm faces of an arrangement ofn lines
in the plane isO(m 2/3– n 2/3+2 +n) for any>0. The proof takes an algorithmic
approach, that is, we describe an algorithm for the calculation of thesem faces
and derive the upper bound from the analysis of the algorithm. The algorithm uses
randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn
logm). If instead of lines we have an arrangement ofn line segments, then the
maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any>0,
where(n) is the functional inverse of Ackermann's function. We give a (randomized)
algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n)
log2 n logm).
acknowledgement: The first author is pleased to acknowledge partial support by the
Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and the National Science Foundation
under Grant CCR-8714565. Work on this paper by the third author has been supported
by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation
Grant DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM
Corporation, and by a research grant from the NCRD-the Israeli National Council
for Research and Development. A preliminary version of this paper has appeared in
theProceedings of the 4th ACM Symposium on Computational Geometry, 1988, pp. 44–55.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: Edelsbrunner H, Guibas L, Sharir M. The complexity and construction of many
faces in arrangements of lines and of segments. Discrete & Computational
Geometry. 1990;5(1):161-196. doi:10.1007/BF02187784
apa: Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity and construction
of many faces in arrangements of lines and of segments. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/BF02187784
chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity
and Construction of Many Faces in Arrangements of Lines and of Segments.” Discrete
& Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187784.
ieee: H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity and construction
of many faces in arrangements of lines and of segments,” Discrete & Computational
Geometry, vol. 5, no. 1. Springer, pp. 161–196, 1990.
ista: Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity and construction
of many faces in arrangements of lines and of segments. Discrete & Computational
Geometry. 5(1), 161–196.
mla: Edelsbrunner, Herbert, et al. “The Complexity and Construction of Many Faces
in Arrangements of Lines and of Segments.” Discrete & Computational Geometry,
vol. 5, no. 1, Springer, 1990, pp. 161–96, doi:10.1007/BF02187784.
short: H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry
5 (1990) 161–196.
date_created: 2018-12-11T12:06:46Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T09:27:30Z
day: '01'
doi: 10.1007/BF02187784
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187784
month: '01'
oa_version: None
page: 161 - 196
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2053'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The complexity and construction of many faces in arrangements of lines and
of segments
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4073'
abstract:
- lang: eng
text: A number of rendering algorithms in computer graphics sort three-dimensional
objects by depth and assume that there is no cycle that makes the sorting impossible.
One way to resolve the problem caused by cycles is to cut the objects into smaller
pieces. The problem of estimating how many such cuts are always sufficient is
addressed. A few related algorithmic and combinatorial geometry problems are considered.
article_processing_charge: No
author:
- first_name: Bernard
full_name: Chazelle, Bernard
last_name: Chazelle
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Richard
full_name: Pollack, Richard
last_name: Pollack
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Jack
full_name: Snoeyink, Jack
last_name: Snoeyink
citation:
ama: 'Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of
lines and rods in space. In: 31st Annual Symposium on Foundations of Computer
Science. IEEE; 1990:242-251. doi:10.1109/FSCS.1990.89543'
apa: 'Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir,
M., & Snoeyink, J. (1990). Counting and cutting cycles of lines and rods in
space. In 31st Annual Symposium on Foundations of Computer Science (pp.
242–251). St. Louis, MO, United States of America: IEEE. https://doi.org/10.1109/FSCS.1990.89543'
chicago: Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack,
Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles
of Lines and Rods in Space.” In 31st Annual Symposium on Foundations of Computer
Science, 242–51. IEEE, 1990. https://doi.org/10.1109/FSCS.1990.89543.
ieee: B. Chazelle et al., “Counting and cutting cycles of lines and rods
in space,” in 31st Annual Symposium on Foundations of Computer Science,
St. Louis, MO, United States of America, 1990, pp. 242–251.
ista: 'Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink
J. 1990. Counting and cutting cycles of lines and rods in space. 31st Annual Symposium
on Foundations of Computer Science. FOCS: Foundations of Computer Science, 242–251.'
mla: Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in
Space.” 31st Annual Symposium on Foundations of Computer Science, IEEE,
1990, pp. 242–51, doi:10.1109/FSCS.1990.89543.
short: B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir,
J. Snoeyink, in:, 31st Annual Symposium on Foundations of Computer Science, IEEE,
1990, pp. 242–251.
conference:
end_date: 1990-10-24
location: St. Louis, MO, United States of America
name: 'FOCS: Foundations of Computer Science'
start_date: 1990-10-22
date_created: 2018-12-11T12:06:47Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-17T11:07:07Z
day: '01'
doi: 10.1109/FSCS.1990.89543
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/89543
month: '01'
oa_version: None
page: 242 - 251
publication: 31st Annual Symposium on Foundations of Computer Science
publication_identifier:
isbn:
- 0-8186-2082-X
publication_status: published
publisher: IEEE
publist_id: '2047'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting and cutting cycles of lines and rods in space
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4074'
abstract:
- lang: eng
text: We present upper and lower bounds for extremal problems defined for arrangements
of lines, circles, spheres, and alike. For example, we prove that the maximum
number of edges boundingm cells in an arrangement ofn lines is Θ(m 2/3 n 2/3 +n),
and that it isO(m 2/3 n 2/3 β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m,
n)) is a function that depends on the inverse of Ackermann's function and grows
extremely slowly. If we replace unit-circles by circles of arbitrary radii the
upper bound goes up toO(m 3/5 n 4/5 β(n) +n). The same bounds (without theβ(n)-terms)
hold for the maximum sum of degrees ofm vertices. In the case of vertex degrees
in arrangements of lines and of unit-circles our bounds match previous results,
but our proofs are considerably simpler than the previous ones. The maximum sum
of degrees ofm vertices in an arrangement ofn spheres in three dimensions isO(m
4/7 n 9/7 β(m, n) +n 2), in general, andO(m 3/4 n 3/4 β(m, n) +n) if no three
spheres intersect in a common circle. The latter bound implies that the maximum
number of unit-distances amongm points in three dimensions isO(m 3/2 β(m)) which
improves the best previous upper bound on this problem. Applications of our results
to other distance problems are also given.
acknowledgement: The research of the second author was supported by the National Science
Foundation under Grant CCR-8714565. Work by the fourth author has been supported
by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation
Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation and
the IBM Corporation, and by a research grant from the NCRD, the Israeli National
Council for Research and Development. A preliminary version of this paper has appeared
in theProceedings of the 29th IEEE Symposium on Foundations of Computer Science,
1988.
article_processing_charge: No
article_type: original
author:
- first_name: Kenneth
full_name: Clarkson, Kenneth
last_name: Clarkson
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. Combinatorial complexity
bounds for arrangements of curves and spheres. Discrete & Computational
Geometry. 1990;5(1):99-160. doi:10.1007/BF02187783
apa: Clarkson, K., Edelsbrunner, H., Guibas, L., Sharir, M., & Welzl, E. (1990).
Combinatorial complexity bounds for arrangements of curves and spheres. Discrete
& Computational Geometry. Springer. https://doi.org/10.1007/BF02187783
chicago: Clarkson, Kenneth, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir,
and Emo Welzl. “Combinatorial Complexity Bounds for Arrangements of Curves and
Spheres.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187783.
ieee: K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, “Combinatorial
complexity bounds for arrangements of curves and spheres,” Discrete & Computational
Geometry, vol. 5, no. 1. Springer, pp. 99–160, 1990.
ista: Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. 1990. Combinatorial
complexity bounds for arrangements of curves and spheres. Discrete & Computational
Geometry. 5(1), 99–160.
mla: Clarkson, Kenneth, et al. “Combinatorial Complexity Bounds for Arrangements
of Curves and Spheres.” Discrete & Computational Geometry, vol. 5,
no. 1, Springer, 1990, pp. 99–160, doi:10.1007/BF02187783.
short: K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, E. Welzl, Discrete &
Computational Geometry 5 (1990) 99–160.
date_created: 2018-12-11T12:06:47Z
date_published: 1990-03-01T00:00:00Z
date_updated: 2022-02-17T15:41:04Z
day: '01'
doi: 10.1007/BF02187783
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187783
month: '03'
oa_version: None
page: 99 - 160
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2048'
quality_controlled: '1'
status: public
title: Combinatorial complexity bounds for arrangements of curves and spheres
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4075'
abstract:
- lang: eng
text: A key problem in computational geometry is the identification of subsets of
a point set having particular properties. We study this problem for the properties
of convexity and emptiness. We show that finding empty triangles is related to
the problem of determining pairs of vertices that see each other in a star-shaped
polygon. A linear-time algorithm for this problem which is of independent interest
yields an optimal algorithm for finding all empty triangles. This result is then
extended to an algorithm for finding empty convex r-gons (r> 3) and for determining
a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.
acknowledgement: The first author is pleased to acknowledge support by the National
Science Foundation under Grant CCR-8700917. The research of the second author was
supported by Amoco Foundation Faculty Development Grant CS 1-6-44862 and by the
National Science Foundatio
article_processing_charge: No
article_type: original
author:
- first_name: David
full_name: Dobkin, David
last_name: Dobkin
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mark
full_name: Overmars, Mark
last_name: Overmars
citation:
ama: Dobkin D, Edelsbrunner H, Overmars M. Searching for empty convex polygons.
Algorithmica. 1990;5(4):561-571. doi:10.1007/BF01840404
apa: Dobkin, D., Edelsbrunner, H., & Overmars, M. (1990). Searching for empty
convex polygons. Algorithmica. Springer. https://doi.org/10.1007/BF01840404
chicago: Dobkin, David, Herbert Edelsbrunner, and Mark Overmars. “Searching for
Empty Convex Polygons.” Algorithmica. Springer, 1990. https://doi.org/10.1007/BF01840404.
ieee: D. Dobkin, H. Edelsbrunner, and M. Overmars, “Searching for empty convex polygons,”
Algorithmica, vol. 5, no. 4. Springer, pp. 561–571, 1990.
ista: Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons.
Algorithmica. 5(4), 561–571.
mla: Dobkin, David, et al. “Searching for Empty Convex Polygons.” Algorithmica,
vol. 5, no. 4, Springer, 1990, pp. 561–71, doi:10.1007/BF01840404.
short: D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571.
date_created: 2018-12-11T12:06:47Z
date_published: 1990-06-01T00:00:00Z
date_updated: 2022-02-21T10:55:13Z
day: '01'
doi: 10.1007/BF01840404
extern: '1'
intvolume: ' 5'
issue: '4'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF01840404
month: '06'
oa_version: None
page: 561 - 571
publication: Algorithmica
publication_identifier:
eissn:
- 1432-0541
issn:
- 0178-4617
publication_status: published
publisher: Springer
publist_id: '2049'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Searching for empty convex polygons
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4076'
abstract:
- lang: eng
text: We present an algorithm to compute a Euclidean minimum spanning tree of a
given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the
time required to compute a bichromatic closest pair among n red and m blue points
in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves
to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic
closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3,
which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean
minimum spanning tree of N points in E3.
article_processing_charge: No
author:
- first_name: Pankaj
full_name: Agarwal, Pankaj
last_name: Agarwal
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Otfried
full_name: Schwarzkopf, Otfried
last_name: Schwarzkopf
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: 'Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. Euclidean minimum spanning
trees and bichromatic closest pairs. In: Proceedings of the 6th Annual Symposium
on Computational Geometry. ACM; 1990:203-210. doi:10.1145/98524.98567'
apa: 'Agarwal, P., Edelsbrunner, H., Schwarzkopf, O., & Welzl, E. (1990). Euclidean
minimum spanning trees and bichromatic closest pairs. In Proceedings of the
6th annual symposium on Computational geometry (pp. 203–210). Berkeley, CA,
United States: ACM. https://doi.org/10.1145/98524.98567'
chicago: Agarwal, Pankaj, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl.
“ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” In Proceedings
of the 6th Annual Symposium on Computational Geometry, 203–10. ACM, 1990.
https://doi.org/10.1145/98524.98567.
ieee: P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl, “ Euclidean minimum
spanning trees and bichromatic closest pairs,” in Proceedings of the 6th annual
symposium on Computational geometry, Berkeley, CA, United States, 1990, pp.
203–210.
ista: 'Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. 1990. Euclidean minimum
spanning trees and bichromatic closest pairs. Proceedings of the 6th annual symposium
on Computational geometry. SCG: Symposium on Computational Geometry, 203–210.'
mla: Agarwal, Pankaj, et al. “ Euclidean Minimum Spanning Trees and Bichromatic
Closest Pairs.” Proceedings of the 6th Annual Symposium on Computational Geometry,
ACM, 1990, pp. 203–10, doi:10.1145/98524.98567.
short: P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of
the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.
conference:
end_date: 1990-06-09
location: Berkeley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:48Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-16T15:30:22Z
day: '01'
doi: 10.1145/98524.98567
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98567
month: '01'
oa_version: None
page: 203 - 210
publication: Proceedings of the 6th annual symposium on Computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2044'
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' Euclidean minimum spanning trees and bichromatic closest pairs'
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4077'
abstract:
- lang: eng
text: We prove that for any set S of n points in the plane and n3-α triangles spanned
by the points of S there exists a point (not necessarily of S) contained in at
least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points
in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.
article_processing_charge: No
author:
- first_name: Boris
full_name: Aronov, Boris
last_name: Aronov
- first_name: Bernard
full_name: Chazelle, Bernard
last_name: Chazelle
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Rephael
full_name: Wenger, Rephael
last_name: Wenger
citation:
ama: 'Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points
and triangles in the plane and halving planes in space. In: Proceedings of
the 6th Annual Symposium on Computational Geometry. ACM; 1990:112-115. doi:10.1145/98524.98548'
apa: 'Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &
Wenger, R. (1990). Points and triangles in the plane and halving planes in space.
In Proceedings of the 6th annual symposium on Computational geometry (pp.
112–115). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98548'
chicago: Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas,
Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving
Planes in Space.” In Proceedings of the 6th Annual Symposium on Computational
Geometry, 112–15. ACM, 1990. https://doi.org/10.1145/98524.98548.
ieee: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger,
“Points and triangles in the plane and halving planes in space,” in Proceedings
of the 6th annual symposium on Computational geometry, Berkley, CA, United
States, 1990, pp. 112–115.
ista: 'Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990.
Points and triangles in the plane and halving planes in space. Proceedings of
the 6th annual symposium on Computational geometry. SCG: Symposium on Computational
Geometry, 112–115.'
mla: Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes
in Space.” Proceedings of the 6th Annual Symposium on Computational Geometry,
ACM, 1990, pp. 112–15, doi:10.1145/98524.98548.
short: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger,
in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990,
pp. 112–115.
conference:
end_date: 1990-06-09
location: Berkley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:48Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-17T09:42:27Z
day: '01'
doi: 10.1145/98524.98548
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98548
month: '01'
oa_version: None
page: 112 - 115
publication: Proceedings of the 6th annual symposium on Computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2045'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Points and triangles in the plane and halving planes in space
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4078'
abstract:
- lang: eng
text: In this paper we derived combinatorial point selection results for geometric
objects defined by pairs of points. In a nutshell, the results say that if many
pairs of a set of n points in some fixed dimension each define a geometric object
of some type, then there is a point covered by many of these objects. Based on
such a result for three-dimensional spheres we show that the combinatorial size
of the Delaunay triangulation of a point set in space can be reduced by adding
new points. We believe that from a practical point of view this is the most important
result of this paper.
article_processing_charge: No
author:
- first_name: Bernard
full_name: Chazelle, Bernard
last_name: Chazelle
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: John
full_name: Hershberger, John
last_name: Hershberger
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: 'Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M. Slimming
down by adding; selecting heavily covered points. In: Proceedings of the 6th
Annual Symposium on Computational Geometry. ACM; 1990:116-127. doi:10.1145/98524.98551'
apa: 'Chazelle, B., Edelsbrunner, H., Guibas, L., Hershberger, J., Seidel, R., &
Sharir, M. (1990). Slimming down by adding; selecting heavily covered points.
In Proceedings of the 6th annual symposium on computational geometry (pp.
116–127). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98551'
chicago: Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, John Hershberger,
Raimund Seidel, and Micha Sharir. “Slimming down by Adding; Selecting Heavily
Covered Points.” In Proceedings of the 6th Annual Symposium on Computational
Geometry, 116–27. ACM, 1990. https://doi.org/10.1145/98524.98551.
ieee: B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, and M.
Sharir, “Slimming down by adding; selecting heavily covered points,” in Proceedings
of the 6th annual symposium on computational geometry, Berkley, CA, United
States, 1990, pp. 116–127.
ista: 'Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M.
1990. Slimming down by adding; selecting heavily covered points. Proceedings of
the 6th annual symposium on computational geometry. SCG: Symposium on Computational
Geometry, 116–127.'
mla: Chazelle, Bernard, et al. “Slimming down by Adding; Selecting Heavily Covered
Points.” Proceedings of the 6th Annual Symposium on Computational Geometry,
ACM, 1990, pp. 116–27, doi:10.1145/98524.98551.
short: B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, M. Sharir,
in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990,
pp. 116–127.
conference:
end_date: 1990-06-09
location: Berkley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:48Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-17T10:09:54Z
day: '01'
doi: 10.1145/98524.98551
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98551
month: '01'
oa_version: None
page: 116 - 127
publication: Proceedings of the 6th annual symposium on computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2046'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Slimming down by adding; selecting heavily covered points
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4310'
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Steve
full_name: Jones, Steve
last_name: Jones
citation:
ama: Barton NH, Jones S. The language of the genes. Nature. 1990;346:415-416.
doi:10.1038/346415a0
apa: Barton, N. H., & Jones, S. (1990). The language of the genes. Nature.
Nature Publishing Group. https://doi.org/10.1038/346415a0
chicago: Barton, Nicholas H, and Steve Jones. “The Language of the Genes.” Nature.
Nature Publishing Group, 1990. https://doi.org/10.1038/346415a0.
ieee: N. H. Barton and S. Jones, “The language of the genes,” Nature, vol.
346. Nature Publishing Group, pp. 415–416, 1990.
ista: Barton NH, Jones S. 1990. The language of the genes. Nature. 346, 415–416.
mla: Barton, Nicholas H., and Steve Jones. “The Language of the Genes.” Nature,
vol. 346, Nature Publishing Group, 1990, pp. 415–16, doi:10.1038/346415a0.
short: N.H. Barton, S. Jones, Nature 346 (1990) 415–416.
date_created: 2018-12-11T12:08:11Z
date_published: 1990-08-02T00:00:00Z
date_updated: 2022-02-16T10:51:50Z
day: '02'
doi: 10.1038/346415a0
extern: '1'
intvolume: ' 346'
language:
- iso: eng
main_file_link:
- url: https://www.nature.com/articles/346415a0
month: '08'
oa_version: None
page: 415 - 416
publication: Nature
publication_identifier:
eissn:
- 1476-4687
issn:
- 0028-0836
publication_status: published
publisher: Nature Publishing Group
publist_id: '1749'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The language of the genes
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 346
year: '1990'
...
---
_id: '4311'
article_processing_charge: No
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: A.
full_name: Clark, A.
last_name: Clark
citation:
ama: 'Barton NH, Clark A. Population structure and processes in evolution. In: Wöhrmann
K, Jain S, eds. Population Biology: Ecological and Evolutionary Viewpoints.
Springer; 1990:115-174. doi:10.1007/978-3-642-74474-7_5'
apa: 'Barton, N. H., & Clark, A. (1990). Population structure and processes
in evolution. In K. Wöhrmann & S. Jain (Eds.), Population biology: Ecological
and evolutionary viewpoints (pp. 115–174). Springer. https://doi.org/10.1007/978-3-642-74474-7_5'
chicago: 'Barton, Nicholas H, and A. Clark. “Population Structure and Processes
in Evolution.” In Population Biology: Ecological and Evolutionary Viewpoints,
edited by Klaus Wöhrmann and Subodh Jain, 115–74. Springer, 1990. https://doi.org/10.1007/978-3-642-74474-7_5.'
ieee: 'N. H. Barton and A. Clark, “Population structure and processes in evolution,”
in Population biology: Ecological and evolutionary viewpoints, K. Wöhrmann
and S. Jain, Eds. Springer, 1990, pp. 115–174.'
ista: 'Barton NH, Clark A. 1990.Population structure and processes in evolution.
In: Population biology: Ecological and evolutionary viewpoints. , 115–174.'
mla: 'Barton, Nicholas H., and A. Clark. “Population Structure and Processes in
Evolution.” Population Biology: Ecological and Evolutionary Viewpoints,
edited by Klaus Wöhrmann and Subodh Jain, Springer, 1990, pp. 115–74, doi:10.1007/978-3-642-74474-7_5.'
short: 'N.H. Barton, A. Clark, in:, K. Wöhrmann, S. Jain (Eds.), Population Biology:
Ecological and Evolutionary Viewpoints, Springer, 1990, pp. 115–174.'
date_created: 2018-12-11T12:08:11Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-16T10:49:05Z
day: '01'
doi: 10.1007/978-3-642-74474-7_5
editor:
- first_name: Klaus
full_name: Wöhrmann, Klaus
last_name: Wöhrmann
- first_name: Subodh
full_name: Jain, Subodh
last_name: Jain
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/book/10.1007/978-3-642-74474-7
month: '01'
oa_version: None
page: 115 - 174
publication: 'Population biology: Ecological and evolutionary viewpoints'
publication_identifier:
isbn:
- ' 978-3642744761'
publication_status: published
publisher: Springer
publist_id: '1748'
quality_controlled: '1'
status: public
title: Population structure and processes in evolution
type: book_chapter
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...
---
_id: '4510'
abstract:
- lang: eng
text: "The interleaving model is both adequate and sufficiently abstract to allow
for the practical specification and verification of many properties of concurrent
systems. We incorporate real time into this model by defining the abstract notion
of a real-time transition system as a conservative extension of traditional transition
systems: qualitative fairness requirements are replaced (and superseded) by quantitative
lower-bound and upper-bound real-time requirements for transitions.\r\nWe present
proof rules to establish lower and upper real-time bounds for response properties
of real-time transition systems. This proof system can be used to verify bounded-invariance
and bounded-response properties, such as timely termination of shared-variables
multi-process systems, whose semantics is defined in terms of real-time transition
systems."
acknowledgement: 'Sponsors: IBM graduate fellowship, National Science Foundation
grant CCR-89-11512, National Science Foundation CCR-89-13641, Defense Advanced
Research Projects Agency under contract N00039-84-C-0211, United States Air Force
Office of Scientific Research under contract AFOSR-90-0057, European Community
ESPRIT Basic Research Action project 3096 (SPEC).'
article_processing_charge: No
author:
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Zohar
full_name: Manna, Zohar
last_name: Manna
- first_name: Amir
full_name: Pnueli, Amir
last_name: Pnueli
citation:
ama: 'Henzinger TA, Manna Z, Pnueli A. An interleaving model for real time. In:
Proceedings of the 5th Jerusalem Conference on Information Technology.
IEEE; 1990:717-730. doi:10.1109/JCIT.1990.128356'
apa: 'Henzinger, T. A., Manna, Z., & Pnueli, A. (1990). An interleaving model
for real time. In Proceedings of the 5th Jerusalem Conference on Information
Technology (pp. 717–730). Jerusalem, Israel: IEEE. https://doi.org/10.1109/JCIT.1990.128356'
chicago: Henzinger, Thomas A, Zohar Manna, and Amir Pnueli. “An Interleaving Model
for Real Time.” In Proceedings of the 5th Jerusalem Conference on Information
Technology, 717–30. IEEE, 1990. https://doi.org/10.1109/JCIT.1990.128356.
ieee: T. A. Henzinger, Z. Manna, and A. Pnueli, “An interleaving model for real
time,” in Proceedings of the 5th Jerusalem Conference on Information Technology,
Jerusalem, Israel, 1990, pp. 717–730.
ista: 'Henzinger TA, Manna Z, Pnueli A. 1990. An interleaving model for real time. Proceedings
of the 5th Jerusalem Conference on Information Technology. JCIT: Jerusalem Conference
on Information Technology, 717–730.'
mla: Henzinger, Thomas A., et al. “An Interleaving Model for Real Time.” Proceedings
of the 5th Jerusalem Conference on Information Technology, IEEE, 1990, pp.
717–30, doi:10.1109/JCIT.1990.128356.
short: T.A. Henzinger, Z. Manna, A. Pnueli, in:, Proceedings of the 5th Jerusalem
Conference on Information Technology, IEEE, 1990, pp. 717–730.
conference:
end_date: 1990-10-25
location: Jerusalem, Israel
name: 'JCIT: Jerusalem Conference on Information Technology'
start_date: 1990-10-22
date_created: 2018-12-11T12:09:14Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-15T15:51:25Z
day: '01'
doi: 10.1109/JCIT.1990.128356
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/abstract/document/128356
month: '01'
oa_version: None
page: 717 - 730
publication: ' Proceedings of the 5th Jerusalem Conference on Information Technology'
publication_identifier:
isbn:
- 0-8186-2078-1
publication_status: published
publisher: IEEE
publist_id: '220'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An interleaving model for real time
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...