Paper by Erik D. Demaine

Reference:

Prosenjit Bose, Erik D. Demaine, Ferran Hurtado, John Iacono, Stefan Langerman, and Pat Morin, “Geodesic Ham-Sandwich Cuts”, in Proceedings of the 20th Annual ACM Symposium on Computational Geometry (SoCG 2004), Brooklyn, New York, June 9–11, 2004, pages 1–9.

BibTeX

@InProceedings{GeodesicHamSandwich_SoCG2004,
  AUTHOR        = {Prosenjit Bose and Erik D. Demaine and Ferran Hurtado and
                   John Iacono and Stefan Langerman and Pat Morin},
  TITLE         = {Geodesic Ham-Sandwich Cuts},
  BOOKTITLE     = {Proceedings of the 20th Annual ACM Symposium on
                   Computational Geometry (SoCG 2004)},
  bookurl       = {http://socg.poly.edu/home.htm},
  MONTH         = {June 9--11},
  YEAR          = 2004,
  ADDRESS       = {Brooklyn, New York},
  PAGES         = {1--9},

  length        = {9 pages},
  doi           = {https://dx.doi.org/10.1145/997817.997821},
  dblp          = {https://dblp.org/rec/conf/compgeom/BoseDHILM04},
  comments      = {This paper is also available from the
                   <A HREF="http://doi.acm.org/10.1145/997817.997821">ACM Digital Library</A>.},
  papers        = {GeodesicHamSandwich_DCG},
}

Abstract:

Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m + r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

Comments:

This paper is also available from the ACM Digital Library.

Length:

The paper is 9 pages.

Availability:

The paper is available in PostScript (809k), gzipped PostScript (280k), and PDF (275k).

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Related papers:

GeodesicHamSandwich_DCG (Geodesic Ham-Sandwich Cuts)