---
_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'
...
---
_id: '4522'
abstract:
- lang: eng
text: 'We introduce a novel extension of propositional modal logic that is interpreted
over Kripke structures in which a value is associated with every possible world.
These values are. however, not treated as full first-order objects: they can be
accessed only by a very restricted form of quantification: the "freeze" quantifier
binds a variable to the value of the current world. We present a complete proof
system for this ("half-order") modal logic. As a special case, we obtain the real-time
temporal logic TPTL of [AH891: the models are restricted to infinite sequences
of states, whose values are monotonically increasing natural numbers. The ordering
relation between states is interpreted as temporal precedence. while the value
associated with a state is interpreted as its "rear time. We extend our proof
system to be complete for TPTL. and demonstrate how it can be used to derive real-time
properties. '
acknowledgement: Many thanks to Rajeev Alur, Adam Grove, Zohar Manna, and Amir Pnueli
for their continuous discussions and support.
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
citation:
ama: 'Henzinger TA. Half-order modal logic: How to prove real-time properties. In:
Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing.
ACM; 1990:281-296. doi:10.1145/93385.93429'
apa: 'Henzinger, T. A. (1990). Half-order modal logic: How to prove real-time properties.
In Proceedings of the 9th annual ACM symposium on Principles of distributed
computing (pp. 281–296). Quebec City, Canada: ACM. https://doi.org/10.1145/93385.93429'
chicago: 'Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.”
In Proceedings of the 9th Annual ACM Symposium on Principles of Distributed
Computing, 281–96. ACM, 1990. https://doi.org/10.1145/93385.93429.'
ieee: 'T. A. Henzinger, “Half-order modal logic: How to prove real-time properties,”
in Proceedings of the 9th annual ACM symposium on Principles of distributed
computing, Quebec City, Canada, 1990, pp. 281–296.'
ista: 'Henzinger TA. 1990. Half-order modal logic: How to prove real-time properties.
Proceedings of the 9th annual ACM symposium on Principles of distributed computing.
PODC: Principles of Distributed Computing, 281–296.'
mla: 'Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.”
Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing,
ACM, 1990, pp. 281–96, doi:10.1145/93385.93429.'
short: T.A. Henzinger, in:, Proceedings of the 9th Annual ACM Symposium on Principles
of Distributed Computing, ACM, 1990, pp. 281–296.
conference:
end_date: 1990-08-24
location: Quebec City, Canada
name: 'PODC: Principles of Distributed Computing'
start_date: 1990-08-22
date_created: 2018-12-11T12:09:17Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-15T15:11:03Z
day: '01'
doi: 10.1145/93385.93429
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/93385.93429
month: '01'
oa_version: None
page: 281 - 296
publication: Proceedings of the 9th annual ACM symposium on Principles of distributed
computing
publication_identifier:
isbn:
- 978-0-89791-404-8
publication_status: published
publisher: ACM
publist_id: '209'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Half-order modal logic: How to prove real-time properties'
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...