Standard
Tukey Depth Histograms. / Bertschinger, Daniel; Passweg, Jonas; Schnider, Patrick.
Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings. ed. / Cristina Bazgan; Henning Fernau. Springer, 2022. p. 186-198 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13270 LNCS).
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Harvard
Bertschinger, D, Passweg, J & Schnider, P 2022,
Tukey Depth Histograms. in C Bazgan & H Fernau (eds),
Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13270 LNCS, pp. 186-198, 33rd International Workshop on Combinatorial Algorithms, IWOCA 2022, Trier, Germany,
07/06/2022.
https://doi.org/10.1007/978-3-031-06678-8_14APA
Bertschinger, D., Passweg, J., & Schnider, P. (2022).
Tukey Depth Histograms. In C. Bazgan, & H. Fernau (Eds.),
Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings (pp. 186-198). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 13270 LNCS
https://doi.org/10.1007/978-3-031-06678-8_14Vancouver
Bertschinger D, Passweg J, Schnider P.
Tukey Depth Histograms. In Bazgan C, Fernau H, editors, Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings. Springer. 2022. p. 186-198. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13270 LNCS).
https://doi.org/10.1007/978-3-031-06678-8_14Author
Bertschinger, Daniel ; Passweg, Jonas ; Schnider, Patrick. / Tukey Depth Histograms. Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings. editor / Cristina Bazgan ; Henning Fernau. Springer, 2022. pp. 186-198 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13270 LNCS).
Bibtex
@inproceedings{1272738c403d4d47a8051bbfedd5f42f,
title = "Tukey Depth Histograms",
abstract = "Combinatorial representations of point sets play an important role in discrete and computational geometry. In this work, we investigate a new combinatorial quantity of a point set, called Tukey depth histogram. The Tukey depth histogram of k-flats in Rd with respect to a point set P, is a vector Dk,d(P), whose i{\textquoteright}th entry Dik,d(P) denotes the number of k-flats spanned by k+ 1 points of P that have Tukey depth i with respect to P. It turns out that several problems in discrete and computational geometry can be phrased in terms of such depth histograms. As our main result, we give a complete characterization of the depth histograms of points, that is, for any dimension d we give a description of all possible histograms D0,d(P). This then allows us to compute the exact number of different histograms of points.",
keywords = "Computational geometry, Depth statistics, Point sets, Tukey depth",
author = "Daniel Bertschinger and Jonas Passweg and Patrick Schnider",
note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.; 33rd International Workshop on Combinatorial Algorithms, IWOCA 2022 ; Conference date: 07-06-2022 Through 09-06-2022",
year = "2022",
doi = "10.1007/978-3-031-06678-8_14",
language = "English",
isbn = "9783031066771",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "186--198",
editor = "Cristina Bazgan and Henning Fernau",
booktitle = "Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings",
address = "Switzerland",
}
RIS
TY - GEN
T1 - Tukey Depth Histograms
AU - Bertschinger, Daniel
AU - Passweg, Jonas
AU - Schnider, Patrick
N1 - Publisher Copyright:
© 2022, Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Combinatorial representations of point sets play an important role in discrete and computational geometry. In this work, we investigate a new combinatorial quantity of a point set, called Tukey depth histogram. The Tukey depth histogram of k-flats in Rd with respect to a point set P, is a vector Dk,d(P), whose i’th entry Dik,d(P) denotes the number of k-flats spanned by k+ 1 points of P that have Tukey depth i with respect to P. It turns out that several problems in discrete and computational geometry can be phrased in terms of such depth histograms. As our main result, we give a complete characterization of the depth histograms of points, that is, for any dimension d we give a description of all possible histograms D0,d(P). This then allows us to compute the exact number of different histograms of points.
AB - Combinatorial representations of point sets play an important role in discrete and computational geometry. In this work, we investigate a new combinatorial quantity of a point set, called Tukey depth histogram. The Tukey depth histogram of k-flats in Rd with respect to a point set P, is a vector Dk,d(P), whose i’th entry Dik,d(P) denotes the number of k-flats spanned by k+ 1 points of P that have Tukey depth i with respect to P. It turns out that several problems in discrete and computational geometry can be phrased in terms of such depth histograms. As our main result, we give a complete characterization of the depth histograms of points, that is, for any dimension d we give a description of all possible histograms D0,d(P). This then allows us to compute the exact number of different histograms of points.
KW - Computational geometry
KW - Depth statistics
KW - Point sets
KW - Tukey depth
UR - http://www.scopus.com/inward/record.url?scp=85131914605&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-06678-8_14
DO - 10.1007/978-3-031-06678-8_14
M3 - Article in proceedings
AN - SCOPUS:85131914605
SN - 9783031066771
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 186
EP - 198
BT - Combinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings
A2 - Bazgan, Cristina
A2 - Fernau, Henning
PB - Springer
T2 - 33rd International Workshop on Combinatorial Algorithms, IWOCA 2022
Y2 - 7 June 2022 through 9 June 2022
ER -
