Bipartite diameter and other measures under translation

Boris Aronov; Omrit Filtser; Matthew J. Katz; Khadijeh Sheikhan

doi:10.4230/LIPIcs.STACS.2019.8

Bipartite diameter and other measures under translation

Boris Aronov, Omrit Filtser, Matthew J. Katz, Khadijeh Sheikhan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let A and B be two sets of points in R^d, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).

Original language	English
Title of host publication	36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
Editors	Rolf Niedermeier, Christophe Paul
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771009
DOIs	https://doi.org/10.4230/LIPIcs.STACS.2019.8
State	Published - 1 Mar 2019
Externally published	Yes
Event	36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 - Berlin, Germany Duration: 13 Mar 2019 → 16 Mar 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	126
ISSN (Print)	1868-8969

Conference

Conference	36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
Country/Territory	Germany
City	Berlin
Period	13/03/19 → 16/03/19

Bibliographical note

Publisher Copyright:
© Boris Aronov, Omrit Filtser, Matthew J. Katz, and Khadijeh Sheikhan.

Keywords

Geometric optimization
Minimum-width annulus
Translation-invariant similarity measures

Access to Document

10.4230/LIPIcs.STACS.2019.8

Cite this

Aronov, B., Filtser, O., Katz, M. J., & Sheikhan, K. (2019). Bipartite diameter and other measures under translation. In R. Niedermeier, & C. Paul (Eds.), 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 Article 8 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 126). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2019.8

Aronov, Boris ; Filtser, Omrit ; Katz, Matthew J. et al. / Bipartite diameter and other measures under translation. 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019. editor / Rolf Niedermeier ; Christophe Paul. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).

@inproceedings{e566b025751447c987abf61e0f593661,

title = "Bipartite diameter and other measures under translation",

abstract = "Let A and B be two sets of points in Rd, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).",

keywords = "Geometric optimization, Minimum-width annulus, Translation-invariant similarity measures",

author = "Boris Aronov and Omrit Filtser and Katz, {Matthew J.} and Khadijeh Sheikhan",

note = "Publisher Copyright: {\textcopyright} Boris Aronov, Omrit Filtser, Matthew J. Katz, and Khadijeh Sheikhan.; 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 ; Conference date: 13-03-2019 Through 16-03-2019",

year = "2019",

month = mar,

day = "1",

doi = "10.4230/LIPIcs.STACS.2019.8",

language = "אנגלית",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Rolf Niedermeier and Christophe Paul",

booktitle = "36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019",

address = "גרמניה",

}

Aronov, B, Filtser, O, Katz, MJ & Sheikhan, K 2019, Bipartite diameter and other measures under translation. in R Niedermeier & C Paul (eds), 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019., 8, Leibniz International Proceedings in Informatics, LIPIcs, vol. 126, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019, Berlin, Germany, 13/03/19. https://doi.org/10.4230/LIPIcs.STACS.2019.8

Bipartite diameter and other measures under translation. / Aronov, Boris; Filtser, Omrit; Katz, Matthew J. et al.
36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019. ed. / Rolf Niedermeier; Christophe Paul. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 8 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 126).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Bipartite diameter and other measures under translation

AU - Aronov, Boris

AU - Filtser, Omrit

AU - Katz, Matthew J.

AU - Sheikhan, Khadijeh

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Let A and B be two sets of points in Rd, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).

AB - Let A and B be two sets of points in Rd, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).

KW - Geometric optimization

KW - Minimum-width annulus

KW - Translation-invariant similarity measures

UR - http://www.scopus.com/inward/record.url?scp=85074924983&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.STACS.2019.8

DO - 10.4230/LIPIcs.STACS.2019.8

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85074924983

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019

A2 - Niedermeier, Rolf

A2 - Paul, Christophe

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019

Y2 - 13 March 2019 through 16 March 2019

ER -

Aronov B, Filtser O, Katz MJ, Sheikhan K. Bipartite diameter and other measures under translation. In Niedermeier R, Paul C, editors, 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 8. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.STACS.2019.8

Bipartite diameter and other measures under translation

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this