On finding a better position of a convex polygon inside a circle to minimize the cutting cost

Syed Ishtiaque Ahmed, Md Mansurul Alam Bhuiyan, Masud Hasan, Ishita Kamal Khan

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

1 Citation (Scopus)

Abstract

The problem of cutting a convex polygon P out of a planar piece of material Q (P is already drawn on Q) with minimum total cutting cost is a well studied problem in computational geometry that has been studied with several variations such as P and Q are convex or non-convex polygons, Q is a circle, and the cuts are line cuts or ray cuts. In this paper, we address this problem without the restriction that P is fixed inside Q and consider the variation where Q is a circle and the cuts are line cuts. We show that if P can be placed inside Q such that P does not contain the center of Q, then placing P in a most cornered position inside Q gives a cutting cost of 6.48 times the optimal. We also give an O(n 2)-time algorithm for finding such a position of P, a problem that may be of independent interest. When any placement of P must contain the center of Q, we show that P can be cut of Q with cost 6.054 times the optimal.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages252-262
Number of pages11
Volume5942 LNCS
DOIs
Publication statusPublished - 25 Mar 2010
Event4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka
Duration: 10 Feb 201012 Feb 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5942 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th International Workshop on Algorithms and Computation, WALCOM 2010
CityDhaka
Period10/2/1012/2/10

Fingerprint

Convex polygon
Circle
Minimise
Costs
Computational geometry
Line
Computational Geometry
Placement
Polygon
Half line
Restriction

Keywords

  • Cornerable and non-cornerable polygon
  • Cutting cost
  • Line cut
  • Most cornered position
  • Polygon cutting

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ahmed, S. I., Bhuiyan, M. M. A., Hasan, M., & Khan, I. K. (2010). On finding a better position of a convex polygon inside a circle to minimize the cutting cost. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5942 LNCS, pp. 252-262). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS). https://doi.org/10.1007/978-3-642-11440-3_23

On finding a better position of a convex polygon inside a circle to minimize the cutting cost. / Ahmed, Syed Ishtiaque; Bhuiyan, Md Mansurul Alam; Hasan, Masud; Khan, Ishita Kamal.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5942 LNCS 2010. p. 252-262 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS).

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

Ahmed, SI, Bhuiyan, MMA, Hasan, M & Khan, IK 2010, On finding a better position of a convex polygon inside a circle to minimize the cutting cost. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5942 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5942 LNCS, pp. 252-262, 4th International Workshop on Algorithms and Computation, WALCOM 2010, Dhaka, 10/2/10. https://doi.org/10.1007/978-3-642-11440-3_23
Ahmed SI, Bhuiyan MMA, Hasan M, Khan IK. On finding a better position of a convex polygon inside a circle to minimize the cutting cost. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5942 LNCS. 2010. p. 252-262. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-11440-3_23
Ahmed, Syed Ishtiaque ; Bhuiyan, Md Mansurul Alam ; Hasan, Masud ; Khan, Ishita Kamal. / On finding a better position of a convex polygon inside a circle to minimize the cutting cost. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5942 LNCS 2010. pp. 252-262 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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