Scandinavian thins on top of cake

On the smallest one-size-fits-all box

Esther M. Arkin, Alon Efrat, George Hart, Irina Kostitsyna, Alexander Kröller, Joseph S B Mitchell, Valentin Polishchuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages16-27
Number of pages12
Volume7288 LNCS
DOIs
StatePublished - 2012
Event6th International Conference on Fun with Algorithms, FUN 2012 - Venice, Italy
Duration: Jun 4 2012Jun 6 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7288 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Conference on Fun with Algorithms, FUN 2012
CountryItaly
CityVenice
Period6/4/126/6/12

Fingerprint

Enclosures
Polygon
Rectangle
Convex polygon
Enclosure
Perimeter
Linear-time Algorithm
Linear Time
NP-complete problem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Arkin, E. M., Efrat, A., Hart, G., Kostitsyna, I., Kröller, A., Mitchell, J. S. B., & Polishchuk, V. (2012). Scandinavian thins on top of cake: On the smallest one-size-fits-all box. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7288 LNCS, pp. 16-27). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7288 LNCS). https://doi.org/10.1007/978-3-642-30347-0_5

Scandinavian thins on top of cake : On the smallest one-size-fits-all box. / Arkin, Esther M.; Efrat, Alon; Hart, George; Kostitsyna, Irina; Kröller, Alexander; Mitchell, Joseph S B; Polishchuk, Valentin.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7288 LNCS 2012. p. 16-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7288 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Arkin, EM, Efrat, A, Hart, G, Kostitsyna, I, Kröller, A, Mitchell, JSB & Polishchuk, V 2012, Scandinavian thins on top of cake: On the smallest one-size-fits-all box. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7288 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7288 LNCS, pp. 16-27, 6th International Conference on Fun with Algorithms, FUN 2012, Venice, Italy, 6/4/12. https://doi.org/10.1007/978-3-642-30347-0_5
Arkin EM, Efrat A, Hart G, Kostitsyna I, Kröller A, Mitchell JSB et al. Scandinavian thins on top of cake: On the smallest one-size-fits-all box. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7288 LNCS. 2012. p. 16-27. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-30347-0_5
Arkin, Esther M. ; Efrat, Alon ; Hart, George ; Kostitsyna, Irina ; Kröller, Alexander ; Mitchell, Joseph S B ; Polishchuk, Valentin. / Scandinavian thins on top of cake : On the smallest one-size-fits-all box. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7288 LNCS 2012. pp. 16-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{c67a1e0a0a484085b352b0e54089b6d2,
title = "Scandinavian thins on top of cake: On the smallest one-size-fits-all box",
abstract = "We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure.",
author = "Arkin, {Esther M.} and Alon Efrat and George Hart and Irina Kostitsyna and Alexander Kr{\"o}ller and Mitchell, {Joseph S B} and Valentin Polishchuk",
year = "2012",
doi = "10.1007/978-3-642-30347-0_5",
language = "English (US)",
isbn = "9783642303463",
volume = "7288 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "16--27",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Scandinavian thins on top of cake

T2 - On the smallest one-size-fits-all box

AU - Arkin, Esther M.

AU - Efrat, Alon

AU - Hart, George

AU - Kostitsyna, Irina

AU - Kröller, Alexander

AU - Mitchell, Joseph S B

AU - Polishchuk, Valentin

PY - 2012

Y1 - 2012

N2 - We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure.

AB - We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure.

UR - http://www.scopus.com/inward/record.url?scp=84861991327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861991327&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-30347-0_5

DO - 10.1007/978-3-642-30347-0_5

M3 - Conference contribution

SN - 9783642303463

VL - 7288 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 16

EP - 27

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -