---
_id: '4098'
abstract:
- lang: eng
text: To points p and q of a finite set S in d-dimensional Euclidean space Ed are
extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum
number of extreme pairs realized by any n points in Ed. We give geometric proofs
of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since
all other cases are trivial.
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: Gerd
full_name: Stöckl, Gerd
last_name: Stöckl
citation:
ama: Edelsbrunner H, Stöckl G. The number of extreme pairs of finite point-sets
in Euclidean spaces. Journal of Combinatorial Theory Series A. 1986;43(2):344-349.
doi:10.1016/0097-3165(86)90075-0
apa: Edelsbrunner, H., & Stöckl, G. (1986). The number of extreme pairs of finite
point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A.
Elsevier. https://doi.org/10.1016/0097-3165(86)90075-0
chicago: Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of
Finite Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series
A. Elsevier, 1986. https://doi.org/10.1016/0097-3165(86)90075-0.
ieee: H. Edelsbrunner and G. Stöckl, “The number of extreme pairs of finite point-sets
in Euclidean spaces,” Journal of Combinatorial Theory Series A, vol. 43,
no. 2. Elsevier, pp. 344–349, 1986.
ista: Edelsbrunner H, Stöckl G. 1986. The number of extreme pairs of finite point-sets
in Euclidean spaces. Journal of Combinatorial Theory Series A. 43(2), 344–349.
mla: Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite
Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series A,
vol. 43, no. 2, Elsevier, 1986, pp. 344–49, doi:10.1016/0097-3165(86)90075-0.
short: H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986)
344–349.
date_created: 2018-12-11T12:06:56Z
date_published: 1986-11-01T00:00:00Z
date_updated: 2022-02-01T14:02:41Z
day: '01'
doi: 10.1016/0097-3165(86)90075-0
extern: '1'
intvolume: ' 43'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0097316586900750?via%3Dihub
month: '11'
oa: 1
oa_version: None
page: 344 - 349
publication: Journal of Combinatorial Theory Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
publist_id: '2020'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The number of extreme pairs of finite point-sets in Euclidean spaces
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 43
year: '1986'
...
---
_id: '4099'
abstract:
- lang: eng
text: Let S denote a set of n points in the Euclidean plane. A halfplanar range
query specifies a halfplane h and requires the determination of the number of
points in S which are contained in h. A new data structure is described which
stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1)
time in the worst case, thus improving the best result known before. The structure
can be built in O(n log n) time.
acknowledgement: 'We thank W. Bucher for help in the analysis of the time complexity
of the query algorithm. '
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: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Welzl E. Halfplanar range search in linear space and O(n0.695)
query time. Information Processing Letters. 1986;23(5):289-293. doi:10.1016/0020-0190(86)90088-8
apa: Edelsbrunner, H., & Welzl, E. (1986). Halfplanar range search in linear
space and O(n0.695) query time. Information Processing Letters. Elsevier.
https://doi.org/10.1016/0020-0190(86)90088-8
chicago: Edelsbrunner, Herbert, and Emo Welzl. “Halfplanar Range Search in Linear
Space and O(N0.695) Query Time.” Information Processing Letters. Elsevier,
1986. https://doi.org/10.1016/0020-0190(86)90088-8.
ieee: H. Edelsbrunner and E. Welzl, “Halfplanar range search in linear space and
O(n0.695) query time,” Information Processing Letters, vol. 23, no. 5.
Elsevier, pp. 289–293, 1986.
ista: Edelsbrunner H, Welzl E. 1986. Halfplanar range search in linear space and
O(n0.695) query time. Information Processing Letters. 23(5), 289–293.
mla: Edelsbrunner, Herbert, and Emo Welzl. “Halfplanar Range Search in Linear Space
and O(N0.695) Query Time.” Information Processing Letters, vol. 23, no.
5, Elsevier, 1986, pp. 289–93, doi:10.1016/0020-0190(86)90088-8.
short: H. Edelsbrunner, E. Welzl, Information Processing Letters 23 (1986) 289–293.
date_created: 2018-12-11T12:06:56Z
date_published: 1986-11-24T00:00:00Z
date_updated: 2022-02-01T14:17:10Z
day: '24'
doi: 10.1016/0020-0190(86)90088-8
extern: '1'
intvolume: ' 23'
issue: '5'
language:
- iso: eng
month: '11'
oa_version: None
page: 289 - 293
publication: Information Processing Letters
publication_identifier:
eissn:
- 1872-6119
issn:
- 0020-0190
publication_status: published
publisher: Elsevier
publist_id: '2021'
quality_controlled: '1'
status: public
title: Halfplanar range search in linear space and O(n0.695) query time
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 23
year: '1986'
...
---
_id: '4103'
abstract:
- lang: eng
text: Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces
in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic
bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces
in an arrangement of n lines. The results improve known bounds for k of higher
order than n(1/2).
acknowledgement: The second author thanks Gan Gusfield for useful discussion.
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: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Welzl E. On the maximal number of edges of many faces in an
arrangement. Journal of Combinatorial Theory Series A. 1986;41(2):159-166.
doi:10.1016/0097-3165(86)90078-6
apa: Edelsbrunner, H., & Welzl, E. (1986). On the maximal number of edges of
many faces in an arrangement. Journal of Combinatorial Theory Series A.
Elsevier. https://doi.org/10.1016/0097-3165(86)90078-6
chicago: Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of
Many Faces in an Arrangement.” Journal of Combinatorial Theory Series A.
Elsevier, 1986. https://doi.org/10.1016/0097-3165(86)90078-6.
ieee: H. Edelsbrunner and E. Welzl, “On the maximal number of edges of many faces
in an arrangement,” Journal of Combinatorial Theory Series A, vol. 41,
no. 2. Elsevier, pp. 159–166, 1986.
ista: Edelsbrunner H, Welzl E. 1986. On the maximal number of edges of many faces
in an arrangement. Journal of Combinatorial Theory Series A. 41(2), 159–166.
mla: Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of Many
Faces in an Arrangement.” Journal of Combinatorial Theory Series A, vol.
41, no. 2, Elsevier, 1986, pp. 159–66, doi:10.1016/0097-3165(86)90078-6.
short: H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 41 (1986)
159–166.
date_created: 2018-12-11T12:06:57Z
date_published: 1986-11-01T00:00:00Z
date_updated: 2022-02-01T09:46:55Z
day: '01'
doi: 10.1016/0097-3165(86)90078-6
extern: '1'
intvolume: ' 41'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0097316586900786?via%3Dihub
month: '11'
oa: 1
oa_version: Published Version
page: 159 - 166
publication: Journal of Combinatorial Theory Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
publist_id: '2015'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the maximal number of edges of many faces in an arrangement
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 41
year: '1986'
...
---
_id: '4104'
abstract:
- lang: eng
text: "Point location, often known in graphics as “hit detection,” is one of the
fundamental problems of computational geometry. In a point location query we want
to identify which of a given collection of geometric objects contains a particular
point. Let $\\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone
regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial
refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp.
594–606] for locating a point in $\\mathcal{S}$ based on separating chains. The
new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$
storage, and makes possible point location in $O(\\log m)$ time. Unlike previous
structures that attain these optimal bounds, the layered dag can be implemented
in a simple and practical way, and is extensible to subdivisions with edges more
general than straight-line segments.\r\n© 1986 Society for Industrial and Applied
Mathematics"
acknowledgement: We would like to thank Andrei Broder, Dan Greene, Mary Claire van
Leunen, Greg Nelson, Lyle Ramshaw, and F. Frances Yao, whose comments and suggestions
have greatly improved the readability of this paper.
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: Jorge
full_name: Stolfi, Jorge
last_name: Stolfi
citation:
ama: Edelsbrunner H, Guibas L, Stolfi J. Optimal point location in a monotone subdivision.
SIAM Journal on Computing. 1986;15(2):317-340. doi:10.1137/0215023
apa: Edelsbrunner, H., Guibas, L., & Stolfi, J. (1986). Optimal point location
in a monotone subdivision. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0215023
chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Jorge Stolfi. “Optimal Point
Location in a Monotone Subdivision.” SIAM Journal on Computing. SIAM, 1986.
https://doi.org/10.1137/0215023.
ieee: H. Edelsbrunner, L. Guibas, and J. Stolfi, “Optimal point location in a monotone
subdivision,” SIAM Journal on Computing, vol. 15, no. 2. SIAM, pp. 317–340,
1986.
ista: Edelsbrunner H, Guibas L, Stolfi J. 1986. Optimal point location in a monotone
subdivision. SIAM Journal on Computing. 15(2), 317–340.
mla: Edelsbrunner, Herbert, et al. “Optimal Point Location in a Monotone Subdivision.”
SIAM Journal on Computing, vol. 15, no. 2, SIAM, 1986, pp. 317–40, doi:10.1137/0215023.
short: H. Edelsbrunner, L. Guibas, J. Stolfi, SIAM Journal on Computing 15 (1986)
317–340.
date_created: 2018-12-11T12:06:58Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T10:05:55Z
day: '01'
doi: 10.1137/0215023
extern: '1'
intvolume: ' 15'
issue: '2'
language:
- iso: eng
month: '01'
oa_version: None
page: 317 - 340
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: SIAM
publist_id: '2016'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal point location in a monotone subdivision
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 15
year: '1986'
...
---
_id: '4105'
abstract:
- lang: eng
text: "A finite set of lines partitions the Euclidean plane into a cell complex.
Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional
Euclidean space. An algorithm is presented that constructs a representation for
the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions.
It relies on a combinatorial result that is of interest in its own right. The
algorithm is shown to lead to new methods for computing $\\lambda $-matrices,
constructing all higher-order Voronoi diagrams, halfspatial range estimation,
degeneracy testing, and finding minimum measure simplices. In all five applications,
the new algorithms are asymptotically faster than previous results, and in several
cases are the only known methods that generalize to arbitrary dimensions. The
algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant,
for the number of combinatorially distinct arrangements of $n$ hyperplanes in
$E^d $.\r\n© 1986 Society for Industrial and Applied Mathematics"
acknowledgement: "We thank Emmerich Welzl for discussions on Theorem 2.7. We also
thank Friedrich Huber for implementing the \r\nconstruction of arrangements in arbitrary
dimensions, and Gerd Stoeckl for implementing the algorithms presented in §§\r\n4.1
and 4.3. The third author wishes to thank Jack Edmonds for the many enlightening
discussions.\r\n"
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: Joseph
full_name: O'Rourke, Joseph
last_name: O'Rourke
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
citation:
ama: Edelsbrunner H, O’Rourke J, Seidel R. Constructing arrangements of lines and
hyperplanes with applications. SIAM Journal on Computing. 1986;15(2):341-363.
doi:10.1137/0215024
apa: Edelsbrunner, H., O’Rourke, J., & Seidel, R. (1986). Constructing arrangements
of lines and hyperplanes with applications. SIAM Journal on Computing.
SIAM. https://doi.org/10.1137/0215024
chicago: Edelsbrunner, Herbert, Joseph O’Rourke, and Raimund Seidel. “Constructing
Arrangements of Lines and Hyperplanes with Applications.” SIAM Journal on Computing.
SIAM, 1986. https://doi.org/10.1137/0215024.
ieee: H. Edelsbrunner, J. O’Rourke, and R. Seidel, “Constructing arrangements of
lines and hyperplanes with applications,” SIAM Journal on Computing, vol.
15, no. 2. SIAM, pp. 341–363, 1986.
ista: Edelsbrunner H, O’Rourke J, Seidel R. 1986. Constructing arrangements of lines
and hyperplanes with applications. SIAM Journal on Computing. 15(2), 341–363.
mla: Edelsbrunner, Herbert, et al. “Constructing Arrangements of Lines and Hyperplanes
with Applications.” SIAM Journal on Computing, vol. 15, no. 2, SIAM, 1986,
pp. 341–63, doi:10.1137/0215024.
short: H. Edelsbrunner, J. O’Rourke, R. Seidel, SIAM Journal on Computing 15 (1986)
341–363.
date_created: 2018-12-11T12:06:58Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T11:03:07Z
day: '01'
doi: 10.1137/0215024
extern: '1'
intvolume: ' 15'
issue: '2'
language:
- iso: eng
month: '01'
oa_version: None
page: 341 - 363
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: SIAM
publist_id: '2017'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Constructing arrangements of lines and hyperplanes with applications
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 15
year: '1986'
...
---
_id: '4106'
abstract:
- lang: eng
text: Let B be a set of nb black points and W a set of nw, white points in the Euclidean
plane. A line h is said to bisect B (or W) if, at most, half of the points of
B (or W) lie on any one side of h. A line that bisects both B and W is called
a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich
cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably
simpler than the previous most efficient one which takes 0((nb + nw) log (nb +
nw)) time.
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: Roman
full_name: Waupotitsch, Roman
last_name: Waupotitsch
citation:
ama: Edelsbrunner H, Waupotitsch R. Computing a ham-sandwich cut in two dimensions.
Journal of Symbolic Computation. 1986;2(2):171-178. doi:10.1016/S0747-7171(86)80020-7
apa: Edelsbrunner, H., & Waupotitsch, R. (1986). Computing a ham-sandwich cut
in two dimensions. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(86)80020-7
chicago: Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich
Cut in Two Dimensions.” Journal of Symbolic Computation. Elsevier, 1986.
https://doi.org/10.1016/S0747-7171(86)80020-7.
ieee: H. Edelsbrunner and R. Waupotitsch, “Computing a ham-sandwich cut in two dimensions,”
Journal of Symbolic Computation, vol. 2, no. 2. Elsevier, pp. 171–178,
1986.
ista: Edelsbrunner H, Waupotitsch R. 1986. Computing a ham-sandwich cut in two dimensions.
Journal of Symbolic Computation. 2(2), 171–178.
mla: Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut
in Two Dimensions.” Journal of Symbolic Computation, vol. 2, no. 2, Elsevier,
1986, pp. 171–78, doi:10.1016/S0747-7171(86)80020-7.
short: H. Edelsbrunner, R. Waupotitsch, Journal of Symbolic Computation 2 (1986)
171–178.
date_created: 2018-12-11T12:06:58Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T11:22:59Z
day: '01'
doi: 10.1016/S0747-7171(86)80020-7
extern: '1'
intvolume: ' 2'
issue: '2'
language:
- iso: eng
month: '01'
oa_version: None
page: 171 - 178
publication: Journal of Symbolic Computation
publication_identifier:
eissn:
- 1095-855X
issn:
- 0747-7171
publication_status: published
publisher: Elsevier
publist_id: '2018'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing a ham-sandwich cut in two dimensions
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2
year: '1986'
...
---
_id: '4107'
abstract:
- lang: eng
text: A set of m planes dissects E3 into cells, facets, edges and vertices. Letting
deg(c) be the number of facets that bound a cellc, we give exact and asymptotic
bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement
with fixed cardinality.
acknowledgement: 'Research reported in the paper was conducted while the second author
was visiting the Technical University of Graz. Support provided by the Technical
University for this visit is gratefully acknowledged. '
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: David
full_name: Haussler, David
last_name: Haussler
citation:
ama: Edelsbrunner H, Haussler D. The complexity of cells in 3-dimensional arrangements.
Discrete Mathematics. 1986;60(C):139-146. doi:10.1016/0012-365X(86)90008-7
apa: Edelsbrunner, H., & Haussler, D. (1986). The complexity of cells in 3-dimensional
arrangements. Discrete Mathematics. Elsevier. https://doi.org/10.1016/0012-365X(86)90008-7
chicago: Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in
3-Dimensional Arrangements.” Discrete Mathematics. Elsevier, 1986. https://doi.org/10.1016/0012-365X(86)90008-7.
ieee: H. Edelsbrunner and D. Haussler, “The complexity of cells in 3-dimensional
arrangements,” Discrete Mathematics, vol. 60, no. C. Elsevier, pp. 139–146,
1986.
ista: Edelsbrunner H, Haussler D. 1986. The complexity of cells in 3-dimensional
arrangements. Discrete Mathematics. 60(C), 139–146.
mla: Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional
Arrangements.” Discrete Mathematics, vol. 60, no. C, Elsevier, 1986, pp.
139–46, doi:10.1016/0012-365X(86)90008-7.
short: H. Edelsbrunner, D. Haussler, Discrete Mathematics 60 (1986) 139–146.
date_created: 2018-12-11T12:06:59Z
date_published: 1986-06-01T00:00:00Z
date_updated: 2022-02-01T12:44:50Z
day: '01'
doi: 10.1016/0012-365X(86)90008-7
extern: '1'
intvolume: ' 60'
issue: C
language:
- iso: eng
month: '06'
oa_version: None
page: 139 - 146
publication: Discrete Mathematics
publication_identifier:
eissn:
- 1872-681X
issn:
- 0012-365X
publication_status: published
publisher: Elsevier
publist_id: '2019'
quality_controlled: '1'
status: public
title: The complexity of cells in 3-dimensional arrangements
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 60
year: '1986'
...
---
_id: '4108'
abstract:
- lang: eng
text: We propose a uniform and general framework for defining and dealing with Voronoi
diagrams. In this framework a Voronoi diagram is a partition of a domainD induced
by a finite number of real valued functions onD. Valuable insight can be gained
when one considers how these real valued functions partitionD ×R. With this view
it turns out that the standard Euclidean Voronoi diagram of point sets inR d along
with its order-k generalizations are intimately related to certain arrangements
of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms.
We also discuss how the formalism of arrangements can be used to solve certain
intersection and union problems.
acknowledgement: 'We would like to thank John Gilbert for his careful reading of the
manuscript and his many suggestions for improvement. We also want to thank Bennett
Battaile, Gianfranco Bilardi, Joseph O''Rourke, and Chee Yap for their comments. '
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: Raimund
full_name: Seidel, Raimund
last_name: Seidel
citation:
ama: Edelsbrunner H, Seidel R. Voronoi diagrams and arrangements. Discrete &
Computational Geometry. 1986;1(1):25-44. doi:10.1007/BF02187681
apa: Edelsbrunner, H., & Seidel, R. (1986). Voronoi diagrams and arrangements.
Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187681
chicago: Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.”
Discrete & Computational Geometry. Springer, 1986. https://doi.org/10.1007/BF02187681.
ieee: H. Edelsbrunner and R. Seidel, “Voronoi diagrams and arrangements,” Discrete
& Computational Geometry, vol. 1, no. 1. Springer, pp. 25–44, 1986.
ista: Edelsbrunner H, Seidel R. 1986. Voronoi diagrams and arrangements. Discrete
& Computational Geometry. 1(1), 25–44.
mla: Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.”
Discrete & Computational Geometry, vol. 1, no. 1, Springer, 1986, pp.
25–44, doi:10.1007/BF02187681.
short: H. Edelsbrunner, R. Seidel, Discrete & Computational Geometry 1 (1986)
25–44.
date_created: 2018-12-11T12:06:59Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T08:53:39Z
day: '01'
doi: 10.1007/BF02187681
extern: '1'
intvolume: ' 1'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 25 - 44
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2012'
quality_controlled: '1'
status: public
title: Voronoi diagrams and arrangements
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 1
year: '1986'
...
---
_id: '4109'
abstract:
- lang: eng
text: Rectangle location search in d dimensions is finding the d-dimensional axis-parallel
box of a non-overlapping collection C that contains a query point. A new data
structure is proposed that requires optimal space and 0(logd|C|) time for a search.
The significance of this data structure in practical applications is substantiated
by empirical examinations of its behaviour.
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: Günter
full_name: Haring, Günter
last_name: Haring
- first_name: D
full_name: Hilbert, D
last_name: Hilbert
citation:
ama: Edelsbrunner H, Haring G, Hilbert D. Rectangular point location in d-dimensions
with applications. Computer Journal. 1986;29(1):76-82. doi:10.1093/comjnl/29.1.76
apa: Edelsbrunner, H., Haring, G., & Hilbert, D. (1986). Rectangular point location
in d-dimensions with applications. Computer Journal. Oxford University
Press. https://doi.org/10.1093/comjnl/29.1.76
chicago: Edelsbrunner, Herbert, Günter Haring, and D Hilbert. “Rectangular Point
Location in D-Dimensions with Applications.” Computer Journal. Oxford University
Press, 1986. https://doi.org/10.1093/comjnl/29.1.76.
ieee: H. Edelsbrunner, G. Haring, and D. Hilbert, “Rectangular point location in
d-dimensions with applications,” Computer Journal, vol. 29, no. 1. Oxford
University Press, pp. 76–82, 1986.
ista: Edelsbrunner H, Haring G, Hilbert D. 1986. Rectangular point location in d-dimensions
with applications. Computer Journal. 29(1), 76–82.
mla: Edelsbrunner, Herbert, et al. “Rectangular Point Location in D-Dimensions with
Applications.” Computer Journal, vol. 29, no. 1, Oxford University Press,
1986, pp. 76–82, doi:10.1093/comjnl/29.1.76.
short: H. Edelsbrunner, G. Haring, D. Hilbert, Computer Journal 29 (1986) 76–82.
date_created: 2018-12-11T12:06:59Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T09:17:51Z
day: '01'
doi: 10.1093/comjnl/29.1.76
extern: '1'
intvolume: ' 29'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 76 - 82
publication: Computer Journal
publication_identifier:
eissn:
- 1460-2067
issn:
- 0010-4620
publication_status: published
publisher: Oxford University Press
publist_id: '2013'
quality_controlled: '1'
status: public
title: Rectangular point location in d-dimensions with applications
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 29
year: '1986'
...
---
_id: '4110'
abstract:
- lang: eng
text: For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection,
called the arrangement of H. We define the notion of a belt in $A(H)$, which is
bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing
belts. All this is motivated by applications to a host of seemingly unrelated
problems including a type of range search and finding the minimum area triangle
with the vertices taken from some finite set of points.
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: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Welzl E. Constructing belts in two-dimensional arrangements
with applications. SIAM Journal on Computing. 1986;15(1):271-284. doi:10.1137/0215019
apa: Edelsbrunner, H., & Welzl, E. (1986). Constructing belts in two-dimensional
arrangements with applications. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0215019
chicago: Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional
Arrangements with Applications.” SIAM Journal on Computing. SIAM, 1986.
https://doi.org/10.1137/0215019.
ieee: H. Edelsbrunner and E. Welzl, “Constructing belts in two-dimensional arrangements
with applications,” SIAM Journal on Computing, vol. 15, no. 1. SIAM, pp.
271–284, 1986.
ista: Edelsbrunner H, Welzl E. 1986. Constructing belts in two-dimensional arrangements
with applications. SIAM Journal on Computing. 15(1), 271–284.
mla: Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional
Arrangements with Applications.” SIAM Journal on Computing, vol. 15, no.
1, SIAM, 1986, pp. 271–84, doi:10.1137/0215019.
short: H. Edelsbrunner, E. Welzl, SIAM Journal on Computing 15 (1986) 271–284.
date_created: 2018-12-11T12:07:00Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T09:34:20Z
day: '01'
doi: 10.1137/0215019
extern: '1'
intvolume: ' 15'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 271 - 284
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: SIAM
publist_id: '2014'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Constructing belts in two-dimensional arrangements with applications
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 15
year: '1986'
...
---
_id: '4321'
abstract:
- lang: eng
text: 'The fire-bellied toads Bombina bombina and B. variegata differ extensively
in biochemistry, morphology, and behavior. We use a survey of five diagnostic
enzyme loci across the hybrid zone near Cracow in Southern Poland to estimate
the dispersal rate, selection pressures, and numbers of loci which maintain this
zone. The enzyme clines coincide closely with each other and with morphological
and mitochondrial DNA clines. Although the zone lies on a broad transition between
environments suitable for bombina and variegata, the close concordance of diverse
characters, together with increased aberrations and mortality in hybrids, suggest
that the zone is maintained largely by selection against hybrids. There are strong
“linkage disequilibria” between each pair of (unlinked) enzyme loci (R̄ = 0.129
[2-unit support limits: 0.119–0.139]). These are probably caused by gene flow
into the zone, and they give an estimate of dispersal (σ = 890 [790–940] m gen−½).
The clines are sharply stepped, with most of the change occurring within 6.15
(5.45–6.45) km, but with long tails of introgression on either side. This implies
that the effective selection pressure on each enzyme marker (due largely to disequilibrium
with other loci) is s* = 0.17 (0.159–0.181) at the center but that the selection
acting directly on the enzyme loci is weak or zero (se < 0.0038). The stepped
pattern implies a barrier to gene flow of 220 (48–415) km. This would substantially
delay neutral introgression but would have little effect on advantageous alleles;
the two taxa need not evolve independently. Strong selection is needed to maintain
such a barrier: hybrid populations must have their mean fitness reduced by a factor
of 0.65 (0.60–0.77). This selection must be spread over a large number of loci
to account for the concordant patterns and the observed cline widths (N = 300
[80–2,000]).'
acknowledgement: 'We are grateful to J. Mitton and W. P. Hall for their suggestions
and help with earlier versions of the statistical analysis. The manuscript was much
improved by the helpful comments of Dorothy Currie, Gunther Gollmann, Godfrey Hewitt,
Julian MacLean, and Jim Mallet. Thanks are also due to Tina Tsang for her careful
typing. This work was supported by the Exchange Agreement between the Polish Academy
of Sciences and the Royal Society, and by grants from the Polish Academy of Sciences
(project MR-II/6), the Royal Society, the Nuffield Foundation, and the Science
and Engineering Research Council. '
article_processing_charge: No
article_type: original
author:
- first_name: Jacek
full_name: Szymura, Jacek
last_name: Szymura
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Szymura J, Barton NH. Genetic analysis of a hybrid zone between the fire-bellied
toads Bombina bombina and B. variegata, near Cracow in Southern Poland. Evolution;
International Journal of Organic Evolution. 1986;40:1141-1159. doi:10.1111/j.1558-5646.1986.tb05740.x
apa: Szymura, J., & Barton, N. H. (1986). Genetic analysis of a hybrid zone
between the fire-bellied toads Bombina bombina and B. variegata, near Cracow in
Southern Poland. Evolution; International Journal of Organic Evolution.
Society for the Study of Evolution. https://doi.org/10.1111/j.1558-5646.1986.tb05740.x
chicago: Szymura, Jacek, and Nicholas H Barton. “Genetic Analysis of a Hybrid Zone
between the Fire-Bellied Toads Bombina Bombina and B. Variegata, near Cracow in
Southern Poland.” Evolution; International Journal of Organic Evolution.
Society for the Study of Evolution, 1986. https://doi.org/10.1111/j.1558-5646.1986.tb05740.x.
ieee: J. Szymura and N. H. Barton, “Genetic analysis of a hybrid zone between the
fire-bellied toads Bombina bombina and B. variegata, near Cracow in Southern Poland,”
Evolution; International Journal of Organic Evolution, vol. 40. Society
for the Study of Evolution, pp. 1141–1159, 1986.
ista: Szymura J, Barton NH. 1986. Genetic analysis of a hybrid zone between the
fire-bellied toads Bombina bombina and B. variegata, near Cracow in Southern Poland.
Evolution; International Journal of Organic Evolution. 40, 1141–1159.
mla: Szymura, Jacek, and Nicholas H. Barton. “Genetic Analysis of a Hybrid Zone
between the Fire-Bellied Toads Bombina Bombina and B. Variegata, near Cracow in
Southern Poland.” Evolution; International Journal of Organic Evolution,
vol. 40, Society for the Study of Evolution, 1986, pp. 1141–59, doi:10.1111/j.1558-5646.1986.tb05740.x.
short: J. Szymura, N.H. Barton, Evolution; International Journal of Organic Evolution
40 (1986) 1141–1159.
date_created: 2018-12-11T12:08:14Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-01-31T15:31:37Z
day: '01'
doi: 10.1111/j.1558-5646.1986.tb05740.x
extern: '1'
intvolume: ' 40'
language:
- iso: eng
month: '01'
oa_version: None
page: 1141 - 1159
publication: Evolution; International Journal of Organic Evolution
publication_identifier:
eissn:
- 1558-5646
issn:
- 0014-3820
publication_status: published
publisher: Society for the Study of Evolution
publist_id: '1724'
quality_controlled: '1'
status: public
title: Genetic analysis of a hybrid zone between the fire-bellied toads Bombina bombina
and B. variegata, near Cracow in Southern Poland
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 40
year: '1986'
...
---
_id: '4323'
abstract:
- lang: eng
text: It is noted that the sibling competition model for the evolution of sex and
recombination, as it has been developed so far, involves truncation selection.
After briefly reviewing aspects of the development and behaviour of such models
an analytical treatment is presented which involves additive selection. Additive
selection, as compared with truncation selection, decreases the advantage of sex
to such an extent that it is unlikely that sibling competition could overcome
its intrinsic two-fold cost, although it could still be important in promoting
family variability produced by other mechanisms, such as polyandry.
acknowledgement: "We would like to thank M. Bulmer for his helpful comments. R. J.
Post was supported during this work by an MRC Postdoctoral Fellowship, and N. Barton
by an SRC Postdoctoral Fellowship. \r\n"
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: R.J.
full_name: Post, R.J.
last_name: Post
citation:
ama: Barton NH, Post RJ. Sibling competition and the advantage of mixed families.
Journal of Theoretical Biology. 1986;120(4):381-387. doi:10.1016/S0022-5193(86)80033-9
apa: Barton, N. H., & Post, R. J. (1986). Sibling competition and the advantage
of mixed families. Journal of Theoretical Biology. Elsevier. https://doi.org/10.1016/S0022-5193(86)80033-9
chicago: Barton, Nicholas H, and R.J. Post. “Sibling Competition and the Advantage
of Mixed Families.” Journal of Theoretical Biology. Elsevier, 1986. https://doi.org/10.1016/S0022-5193(86)80033-9.
ieee: N. H. Barton and R. J. Post, “Sibling competition and the advantage of mixed
families,” Journal of Theoretical Biology, vol. 120, no. 4. Elsevier, pp.
381–387, 1986.
ista: Barton NH, Post RJ. 1986. Sibling competition and the advantage of mixed families.
Journal of Theoretical Biology. 120(4), 381–387.
mla: Barton, Nicholas H., and R. J. Post. “Sibling Competition and the Advantage
of Mixed Families.” Journal of Theoretical Biology, vol. 120, no. 4, Elsevier,
1986, pp. 381–87, doi:10.1016/S0022-5193(86)80033-9.
short: N.H. Barton, R.J. Post, Journal of Theoretical Biology 120 (1986) 381–387.
date_created: 2018-12-11T12:08:15Z
date_published: 1986-06-21T00:00:00Z
date_updated: 2022-01-31T14:44:50Z
day: '21'
doi: 10.1016/S0022-5193(86)80033-9
extern: '1'
intvolume: ' 120'
issue: '4'
language:
- iso: eng
month: '06'
oa_version: None
page: 381 - 387
publication: Journal of Theoretical Biology
publication_identifier:
eissn:
- 1095-8541
issn:
- 0022-5193
publication_status: published
publisher: Elsevier
publist_id: '1720'
quality_controlled: '1'
status: public
title: Sibling competition and the advantage of mixed families
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 120
year: '1986'
...
---
_id: '4324'
abstract:
- lang: eng
text: The maintenance of polygenic variation through a balance between mutation
and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation,
a normal distribution of allelic effects is assumed at each locus. In the ‘House
of Cards’ approximation, the effect of new mutations is assumed to be large compared
with the spread of the existing distribution. These approximations were developed
to describe models where alleles may have a continuous range of effects. However,
previous analyses of models with only two alleles have predicted an equilibrium
variance equal to that given by the ‘House of Cards’ approximation. These analyses
of biallelic models have assumed that, at equilibrium, the population mean is
at the optimum. Here, it is shown that many stable equilibria may coexist, each
giving a slight deviation from the optimum. Though the variance is given by the
‘House of Cards’ approximation when the mean is at the optimum, it increases towards
a value of the same order as that given by the ‘Gaussian’ approximation when the
mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted
by any simple model, but depends on the previous history of the population.
acknowledgement: Thanks are due to J. Felsenstein, J. Gillespie, S. Rouhani, M. Slatkin,
and M. Turelli for stimulating discussions, and for their comments on the manuscript.
This work was sup- ported by a travel grant from the Royal Society, and by a research
grant from the SERC
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
citation:
ama: Barton NH. The maintenance of polygenic variation through a balance between
mutation and stabilising selection. Genetical Research. 1986;47(3):209-216.
doi:10.1017/S0016672300023156
apa: Barton, N. H. (1986). The maintenance of polygenic variation through a balance
between mutation and stabilising selection. Genetical Research. Cambridge
University Press. https://doi.org/10.1017/S0016672300023156
chicago: Barton, Nicholas H. “The Maintenance of Polygenic Variation through a Balance
between Mutation and Stabilising Selection.” Genetical Research. Cambridge
University Press, 1986. https://doi.org/10.1017/S0016672300023156.
ieee: N. H. Barton, “The maintenance of polygenic variation through a balance between
mutation and stabilising selection,” Genetical Research, vol. 47, no. 3.
Cambridge University Press, pp. 209–216, 1986.
ista: Barton NH. 1986. The maintenance of polygenic variation through a balance
between mutation and stabilising selection. Genetical Research. 47(3), 209–216.
mla: Barton, Nicholas H. “The Maintenance of Polygenic Variation through a Balance
between Mutation and Stabilising Selection.” Genetical Research, vol. 47,
no. 3, Cambridge University Press, 1986, pp. 209–16, doi:10.1017/S0016672300023156.
short: N.H. Barton, Genetical Research 47 (1986) 209–216.
date_created: 2018-12-11T12:08:15Z
date_published: 1986-06-01T00:00:00Z
date_updated: 2022-01-31T14:31:48Z
day: '01'
doi: 10.1017/S0016672300023156
extern: '1'
external_id:
pmid:
- '3744046'
intvolume: ' 47'
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 209 - 216
pmid: 1
publication: Genetical Research
publication_identifier:
eissn:
- 1469-5073
issn:
- 0016-6723
publication_status: published
publisher: Cambridge University Press
publist_id: '1718'
quality_controlled: '1'
status: public
title: The maintenance of polygenic variation through a balance between mutation and
stabilising selection
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 47
year: '1986'
...
---
_id: '4111'
abstract:
- lang: eng
text: 'This paper describes an optimal solution for the following geometric search
problem defined for a set P of n points in three dimensions: Given a plane h with
all points of P on one side and a line ℓ in h, determine a point of P that is
hit first when h is rotated around ℓ. The solution takes O(n) space and O(log
n) time for a query. By use of geometric transforms, the post-office problem for
a finite set of points in two dimensions and certain two-dimensional point location
problems are reduced to the former problem and thus also optimally solved.'
acknowledgement: "Research reported in this paper was partially supported by the Austrian
Fonds zur Förderung tier wissenschaftlichen\r\nForschung. \r\n"
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: Hermann
full_name: Maurer, Hermann
last_name: Maurer
citation:
ama: Edelsbrunner H, Maurer H. Finding extreme-points in 3-dimensions and solving
the post-office problem in the plane. Information Processing Letters. 1985;21(1):39-47.
doi:10.1016/0020-0190(85)90107-3
apa: Edelsbrunner, H., & Maurer, H. (1985). Finding extreme-points in 3-dimensions
and solving the post-office problem in the plane. Information Processing Letters.
Elsevier. https://doi.org/10.1016/0020-0190(85)90107-3
chicago: Edelsbrunner, Herbert, and Hermann Maurer. “Finding Extreme-Points in 3-Dimensions
and Solving the Post-Office Problem in the Plane.” Information Processing Letters.
Elsevier, 1985. https://doi.org/10.1016/0020-0190(85)90107-3.
ieee: H. Edelsbrunner and H. Maurer, “Finding extreme-points in 3-dimensions and
solving the post-office problem in the plane,” Information Processing Letters,
vol. 21, no. 1. Elsevier, pp. 39–47, 1985.
ista: Edelsbrunner H, Maurer H. 1985. Finding extreme-points in 3-dimensions and
solving the post-office problem in the plane. Information Processing Letters.
21(1), 39–47.
mla: Edelsbrunner, Herbert, and Hermann Maurer. “Finding Extreme-Points in 3-Dimensions
and Solving the Post-Office Problem in the Plane.” Information Processing Letters,
vol. 21, no. 1, Elsevier, 1985, pp. 39–47, doi:10.1016/0020-0190(85)90107-3.
short: H. Edelsbrunner, H. Maurer, Information Processing Letters 21 (1985) 39–47.
date_created: 2018-12-11T12:07:00Z
date_published: 1985-07-10T00:00:00Z
date_updated: 2022-01-31T12:49:12Z
day: '10'
doi: 10.1016/0020-0190(85)90107-3
extern: '1'
intvolume: ' 21'
issue: '1'
language:
- iso: eng
month: '07'
oa_version: None
page: 39 - 47
publication: Information Processing Letters
publication_identifier:
eissn:
- 1872-6119
issn:
- 0020-0190
publication_status: published
publisher: Elsevier
publist_id: '2009'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finding extreme-points in 3-dimensions and solving the post-office problem
in the plane
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 21
year: '1985'
...
---
_id: '4112'
abstract:
- lang: eng
text: 'The batched static version of a searching problem asks for performing a given
set of queries on a given set of objects. All queries are known in advance. The
batched dynamic version of a searching problem is the following: given a sequence
of insertions, deletions, and queries, perform them on an initially empty set.
We will develop methods for solving batched static and batched dynamic versions
of searching problems which are in particular applicable to decomposable searching
problems. The techniques show that batched static (dynamic) versions of searching
problems can often be solved more efficiently than by using known static (dynamic)
data structures. In particular, a technique called “streaming” is described that
reduces the space requirements considerably. The methods have also a number of
applications on set problems. E.g., the k intersecting pairs in a set of n axis-parallel
hyper-rectangles in d dimensions can be reported in O (nlogd−1n + k) time using
only O(n) space.'
acknowledgement: "Research reported in this paper was done while the second author
visited the University of Graz. The first author was supported by the Austrian Fonds
zur Förderung der Wissenschaftlichen Forschung. The second author was supported
by the Netherlands Organization for the Advancement of Pure Research (ZWO). \r\n"
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: Mark
full_name: Overmars, Mark
last_name: Overmars
citation:
ama: Edelsbrunner H, Overmars M. Batched dynamic solutions to decomposable searching
problems. Journal of Algorithms. 1985;6(4):515-542. doi:10.1016/0196-6774(85)90030-6
apa: Edelsbrunner, H., & Overmars, M. (1985). Batched dynamic solutions to decomposable
searching problems. Journal of Algorithms. Elsevier. https://doi.org/10.1016/0196-6774(85)90030-6
chicago: Edelsbrunner, Herbert, and Mark Overmars. “Batched Dynamic Solutions to
Decomposable Searching Problems.” Journal of Algorithms. Elsevier, 1985.
https://doi.org/10.1016/0196-6774(85)90030-6.
ieee: H. Edelsbrunner and M. Overmars, “Batched dynamic solutions to decomposable
searching problems,” Journal of Algorithms, vol. 6, no. 4. Elsevier, pp.
515–542, 1985.
ista: Edelsbrunner H, Overmars M. 1985. Batched dynamic solutions to decomposable
searching problems. Journal of Algorithms. 6(4), 515–542.
mla: Edelsbrunner, Herbert, and Mark Overmars. “Batched Dynamic Solutions to Decomposable
Searching Problems.” Journal of Algorithms, vol. 6, no. 4, Elsevier, 1985,
pp. 515–42, doi:10.1016/0196-6774(85)90030-6.
short: H. Edelsbrunner, M. Overmars, Journal of Algorithms 6 (1985) 515–542.
date_created: 2018-12-11T12:07:00Z
date_published: 1985-12-01T00:00:00Z
date_updated: 2022-01-31T13:36:56Z
day: '01'
doi: 10.1016/0196-6774(85)90030-6
extern: '1'
intvolume: ' 6'
issue: '4'
language:
- iso: eng
month: '12'
oa_version: None
page: 515 - 542
publication: Journal of Algorithms
publication_identifier:
eissn:
- 1090-2678
issn:
- 0196-6774
publication_status: published
publisher: Elsevier
publist_id: '2010'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Batched dynamic solutions to decomposable searching problems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '1985'
...
---
_id: '4113'
abstract:
- lang: eng
text: Let S denote a set of n points in the Euclidean plane. A subset S′ of S is
termed a k-set of S if it contains k points and there exists a straight line which
has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum
number of k-sets which can be realized by a set of n points. This paper studies
the asymptotic behaviour of fk(n) as this function has applications to a number
of problems in computational geometry. A lower and an upper bound on fk(n) is
established. Both are nontrivial and improve bounds known before. In particular, is
shown by exhibiting special point-sets which realize that many k-sets. In addition, is
proved by the study of a combinatorial problem which is of interest in its own
right.
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: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Welzl E. On the number of line separations of a finite set
in the plane. Journal of Combinatorial Theory Series A. 1985;38(1):15-29.
doi:10.1016/0097-3165(85)90017-2
apa: Edelsbrunner, H., & Welzl, E. (1985). On the number of line separations
of a finite set in the plane. Journal of Combinatorial Theory Series A.
Elsevier. https://doi.org/10.1016/0097-3165(85)90017-2
chicago: Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations
of a Finite Set in the Plane.” Journal of Combinatorial Theory Series A.
Elsevier, 1985. https://doi.org/10.1016/0097-3165(85)90017-2.
ieee: H. Edelsbrunner and E. Welzl, “On the number of line separations of a finite
set in the plane,” Journal of Combinatorial Theory Series A, vol. 38, no.
1. Elsevier, pp. 15–29, 1985.
ista: Edelsbrunner H, Welzl E. 1985. On the number of line separations of a finite
set in the plane. Journal of Combinatorial Theory Series A. 38(1), 15–29.
mla: Edelsbrunner, Herbert, and Emo Welzl. “On the Number of Line Separations of
a Finite Set in the Plane.” Journal of Combinatorial Theory Series A, vol.
38, no. 1, Elsevier, 1985, pp. 15–29, doi:10.1016/0097-3165(85)90017-2.
short: H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 38 (1985)
15–29.
date_created: 2018-12-11T12:07:01Z
date_published: 1985-01-01T00:00:00Z
date_updated: 2022-01-31T14:14:25Z
day: '01'
doi: 10.1016/0097-3165(85)90017-2
extern: '1'
intvolume: ' 38'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 15 - 29
publication: Journal of Combinatorial Theory Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
publist_id: '2011'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of line separations of a finite set in the plane
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 38
year: '1985'
...
---
_id: '4114'
abstract:
- lang: eng
text: Proportional link linkage (PLL) clustering methods are a parametric family
of monotone invariant agglomerative hierarchical clustering methods. This family
includes the single, minimedian, and complete linkage clustering methods as special
cases; its members are used in psychological and ecological applications. Since
the literature on clustering space distortion is oriented to quantitative input
data, we adapt its basic concepts to input data with only ordinal significance
and analyze the space distortion properties of PLL methods. To enable PLL methods
to be used when the numbern of objects being clustered is large, we describe an
efficient PLL algorithm that operates inO(n 2 logn) time andO(n 2) space
acknowledgement: This work was partially supported by the Natural Sciences and Engineering
Research Council of Canada and by the Austrian Fonds zur Förderung der wissenschaftlichen
Forschung.
article_processing_charge: No
article_type: original
author:
- first_name: William
full_name: Day, William
last_name: Day
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Day W, Edelsbrunner H. Investigation of Proportional Link Linkage Clustering
Methods. Journal of Classification. 1985;2(2-3):239-254. doi:10.1007/BF01908077
apa: Day, W., & Edelsbrunner, H. (1985). Investigation of Proportional Link
Linkage Clustering Methods. Journal of Classification. Springer. https://doi.org/10.1007/BF01908077
chicago: Day, William, and Herbert Edelsbrunner. “Investigation of Proportional
Link Linkage Clustering Methods.” Journal of Classification. Springer,
1985. https://doi.org/10.1007/BF01908077.
ieee: W. Day and H. Edelsbrunner, “Investigation of Proportional Link Linkage Clustering
Methods,” Journal of Classification, vol. 2, no. 2–3. Springer, pp. 239–254,
1985.
ista: Day W, Edelsbrunner H. 1985. Investigation of Proportional Link Linkage Clustering
Methods. Journal of Classification. 2(2–3), 239–254.
mla: Day, William, and Herbert Edelsbrunner. “Investigation of Proportional Link
Linkage Clustering Methods.” Journal of Classification, vol. 2, no. 2–3,
Springer, 1985, pp. 239–54, doi:10.1007/BF01908077.
short: W. Day, H. Edelsbrunner, Journal of Classification 2 (1985) 239–254.
date_created: 2018-12-11T12:07:01Z
date_published: 1985-12-01T00:00:00Z
date_updated: 2022-01-31T10:37:13Z
day: '01'
doi: 10.1007/BF01908077
extern: '1'
intvolume: ' 2'
issue: 2-3
language:
- iso: eng
month: '12'
oa_version: None
page: 239 - 254
publication: Journal of Classification
publication_identifier:
eissn:
- 1432-1343
issn:
- 0176-4268
publication_status: published
publisher: Springer
publist_id: '2006'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Investigation of Proportional Link Linkage Clustering Methods
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2
year: '1985'
...
---
_id: '4115'
abstract:
- lang: eng
text: A polygon in the plane is convex if it contains all line segments connecting
any two of its points. Let P and Q denote two convex polygons. The computational
complexity of finding the minimum and maximum distance possible between two points
p in P and q in Q is studied. An algorithm is described that determines the minimum
distance (together with points p and q that realize it) in O(logm + logn) time,
where m and n denote the number of vertices of P and Q, respectively. This is
optimal in the worst case. For computing the maximum distance, a lower bound Ω(m
+ n) is proved. This bound is also shown to be best possible by establishing an
upper bound of O(m + n).
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. Computing the extreme distances between two convex polygons.
Journal of Algorithms. 1985;6(2):213-224. doi:10.1016/0196-6774(85)90039-2
apa: Edelsbrunner, H. (1985). Computing the extreme distances between two convex
polygons. Journal of Algorithms. Academic Press. https://doi.org/10.1016/0196-6774(85)90039-2
chicago: Edelsbrunner, Herbert. “Computing the Extreme Distances between Two Convex
Polygons.” Journal of Algorithms. Academic Press, 1985. https://doi.org/10.1016/0196-6774(85)90039-2.
ieee: H. Edelsbrunner, “Computing the extreme distances between two convex polygons,”
Journal of Algorithms, vol. 6, no. 2. Academic Press, pp. 213–224, 1985.
ista: Edelsbrunner H. 1985. Computing the extreme distances between two convex polygons.
Journal of Algorithms. 6(2), 213–224.
mla: Edelsbrunner, Herbert. “Computing the Extreme Distances between Two Convex
Polygons.” Journal of Algorithms, vol. 6, no. 2, Academic Press, 1985,
pp. 213–24, doi:10.1016/0196-6774(85)90039-2.
short: H. Edelsbrunner, Journal of Algorithms 6 (1985) 213–224.
date_created: 2018-12-11T12:07:01Z
date_published: 1985-06-01T00:00:00Z
date_updated: 2022-01-31T10:44:41Z
day: '01'
doi: 10.1016/0196-6774(85)90039-2
extern: '1'
intvolume: ' 6'
issue: '2'
language:
- iso: eng
month: '06'
oa_version: None
page: 213 - 224
publication: Journal of Algorithms
publication_identifier:
eissn:
- 1090-2678
issn:
- 0196-6774
publication_status: published
publisher: Academic Press
publist_id: '2007'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing the extreme distances between two convex polygons
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '1985'
...
---
_id: '4116'
abstract:
- lang: eng
text: 'A straight line that intersects all members of a set S of objects in the
real plane is called a transversal of S. Geometric transforms are described that
reduce transversal problems for various types of objects to convex hull problems
for points. These reductions lead to efficient algorithms for finding transversals
which are also described. Applications of the algorithms are found in computer
graphics: “Reproduce the line displayed by a collection of pixels”, and in statistics:
“Find the line that minimizes the maximum distance from a collection of (weighted)
points in the plane”.'
acknowledgement: 'The author gratefully acknowledges the criticism of an anonymous
referee who discovered a serious flaw in an earlier version of this paper. '
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. Finding Transversals for Sets of Simple Geometric-Figures.
Theoretical Computer Science. 1985;35(1):55-69. doi:10.1016/0304-3975(85)90005-2
apa: Edelsbrunner, H. (1985). Finding Transversals for Sets of Simple Geometric-Figures.
Theoretical Computer Science. Elsevier. https://doi.org/10.1016/0304-3975(85)90005-2
chicago: Edelsbrunner, Herbert. “Finding Transversals for Sets of Simple Geometric-Figures.”
Theoretical Computer Science. Elsevier, 1985. https://doi.org/10.1016/0304-3975(85)90005-2.
ieee: H. Edelsbrunner, “Finding Transversals for Sets of Simple Geometric-Figures,”
Theoretical Computer Science, vol. 35, no. 1. Elsevier, pp. 55–69, 1985.
ista: Edelsbrunner H. 1985. Finding Transversals for Sets of Simple Geometric-Figures.
Theoretical Computer Science. 35(1), 55–69.
mla: Edelsbrunner, Herbert. “Finding Transversals for Sets of Simple Geometric-Figures.”
Theoretical Computer Science, vol. 35, no. 1, Elsevier, 1985, pp. 55–69,
doi:10.1016/0304-3975(85)90005-2.
short: H. Edelsbrunner, Theoretical Computer Science 35 (1985) 55–69.
date_created: 2018-12-11T12:07:02Z
date_published: 1985-01-01T00:00:00Z
date_updated: 2022-01-31T11:09:26Z
day: '01'
doi: 10.1016/0304-3975(85)90005-2
extern: '1'
intvolume: ' 35'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0304397585900052?via%3Dihub
month: '01'
oa: 1
oa_version: Published Version
page: 55 - 69
publication: Theoretical Computer Science
publication_identifier:
eissn:
- 0304-3975
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
publist_id: '2008'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finding Transversals for Sets of Simple Geometric-Figures
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 35
year: '1985'
...
---
_id: '4120'
abstract:
- lang: eng
text: 'Let P be a set of n points in the Euclidean plane and let C be a convex figure.
We study the problem of preprocessing P so that for any query point q, the points
of P in C+q can be retrieved efficiently. If constant time sumces for deciding
the inclusion of a point in C, we then demonstrate the existence of an optimal
solution: the algorithm requires O(n) space and O(k + log n) time for a query
with output size k. If C is a disk, the problem becomes the wellknown fixed-radius
neighbour problem, to which we thus provide the first known optimal solution.'
acknowledgement: The first author was supported i~1 part by NSF grants MCS 83-03925
and the Office of Naval Research and the Defense Advanced Research Projects Agency
under contract N00014-g3-K-0146 and ARPA Order No. 4786.
article_processing_charge: No
article_type: original
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
citation:
ama: Chazelle B, Edelsbrunner H. Optimal solutions for a class of point retrieval
problems. Journal of Symbolic Computation. 1985;1(1):47-56. doi:10.1016/S0747-7171(85)80028-6
apa: Chazelle, B., & Edelsbrunner, H. (1985). Optimal solutions for a class
of point retrieval problems. Journal of Symbolic Computation. Elsevier.
https://doi.org/10.1016/S0747-7171(85)80028-6
chicago: Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class
of Point Retrieval Problems.” Journal of Symbolic Computation. Elsevier,
1985. https://doi.org/10.1016/S0747-7171(85)80028-6.
ieee: B. Chazelle and H. Edelsbrunner, “Optimal solutions for a class of point retrieval
problems,” Journal of Symbolic Computation, vol. 1, no. 1. Elsevier, pp.
47–56, 1985.
ista: Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval
problems. Journal of Symbolic Computation. 1(1), 47–56.
mla: Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class
of Point Retrieval Problems.” Journal of Symbolic Computation, vol. 1,
no. 1, Elsevier, 1985, pp. 47–56, doi:10.1016/S0747-7171(85)80028-6.
short: B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56.
date_created: 2018-12-11T12:07:03Z
date_published: 1985-03-01T00:00:00Z
date_updated: 2022-01-31T09:20:18Z
day: '01'
doi: 10.1016/S0747-7171(85)80028-6
extern: '1'
intvolume: ' 1'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub
month: '03'
oa: 1
oa_version: Published Version
page: 47 - 56
publication: Journal of Symbolic Computation
publication_identifier:
eissn:
- 1095-855X
issn:
- 0747-7171
publication_status: published
publisher: Elsevier
publist_id: '2004'
quality_controlled: '1'
status: public
title: Optimal solutions for a class of point retrieval problems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 1
year: '1985'
...