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 publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings
Pages252-262
Number of pages11
DOIs
Publication statusPublished - 25 Mar 2010
Event4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka, Bangladesh
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)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Workshop on Algorithms and Computation, WALCOM 2010
CountryBangladesh
CityDhaka
Period10/2/1012/2/10

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • 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 WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings (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