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On Local Transformation of Polygons with Visibility Properties

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Book cover Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

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Abstract

One strategy for the enumeration of a class of objects is local transformation, in which new objects of the class are produced by means of a small modification of a previously-visited object in the same class. When local transformation is possible, the operation can be used to generate objects of the class via random walks, and as the basis for such optimization heuristics as simulated annealing.

For general simple polygons on fixed point sets, it is still not known whether the class of polygons on the set is connected via a constant-size local transformation. In this paper, we exhibit a simple local transformation for which the classes of (weakly) edge-visible and (weakly) externally visible polygons are connected. The latter class is particularly interesting as it is the most general polygon class known to be connected under local transformation.

Partially supported by CUR Gen. Cat. 1999SGR00356 and MEC-DGES-SEUID PB98-0933

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Author information

Authors and Affiliations

  1. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya(UPC), Avda. Diagonal 647, 08028, Barcelona, Spain

    Carmen Hernando

  2. Basser Dept. of Computer Science, The University of Sydney, Sydney, NSW, 2006, Australia

    Michael E. Houle

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya(UPC), Pau Gargallo 5, 08028, Barcelona, Spain

    Ferran Hurtado

Authors
  1. Carmen Hernando
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  2. Michael E. Houle
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  3. Ferran Hurtado
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Hernando, C., Houle, M.E., Hurtado, F. (2000). On Local Transformation of Polygons with Visibility Properties. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_6

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  • DOI: https://doi.org/10.1007/3-540-44968-X_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

  • eBook Packages: Springer Book Archive

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