Dissection with the Fewest Pieces is Hard, Even to Approximate

  • Jeffrey Bosboom
  • Erik D. Demaine
  • Martin L. Demaine
  • Jayson Lynch
  • Pasin Manurangsi
  • Mikhail Rudoy
  • Anak Yodpinyanee
Conference paper

DOI: 10.1007/978-3-319-48532-4_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9943)
Cite this paper as:
Bosboom J. et al. (2016) Dissection with the Fewest Pieces is Hard, Even to Approximate. In: Akiyama J., Ito H., Sakai T., Uno Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science, vol 9943. Springer, Cham

Abstract

We prove that it is NP-hard to dissect one simple orthogonal polygon into another using a given number of pieces, as is approximating the fewest pieces to within a factor of \(1+1/1080-\varepsilon \).

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Jeffrey Bosboom
    • 1
  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Jayson Lynch
    • 1
  • Pasin Manurangsi
    • 2
  • Mikhail Rudoy
    • 1
  • Anak Yodpinyanee
    • 1
  1. 1.Computer Science and AI LaboratoryMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.University of CaliforniaBerkeleyUSA

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