Skip to main content
SpringerLink
Log in

Combinatories and Triangulations

  • Conference paper
Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3045))

Included in the following conference series:

  • 1050 Accesses

Abstract

The problem searching for an optimal triangulation with required properties (in a plane) is solved in this paper. Existing approaches are shortly introduced here and, specially, this paper is dedicated to the brute force methods. Several new brute force methods that solve the problem from different points of view are described here. Although they have NP time complexity, we accelerate the time needed for computation maximally to get results of as large sets of points as possible. Note that our goal is to design the method that can be used for arbitrary criterion without another prerequisite. Therefore, it can serve as a generator of optimal triangulations. For example, those results can be used in verification of developed heuristic methods or in other problems where accurate results are needed and no methods for required criterion have been developed yet.

This work is supported by the Ministry of Education of the Czech Republic projects:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aurenhammer, F.: Voronoi Diagrams - A Survey of a Fundamental Geometric Data Structure. ACM Computing Surveys 23(3), 345–405 (1991)

    Article  Google Scholar 

  2. Drysdale, R., L., S., McElfresh, S., Snoeyink, J., S.: An improved diamond property for minimum weight triangulation (1998)

    Google Scholar 

  3. Ehrlich, G.: Loopless algorithms for generating permutations, combinations, and other combinatorial configurations. Journal of the ACM 20(3), 500–513 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  4. Garey, M., Johnson, R., Computers, D.S.: Intractability: A Guide to the theory of NPcompleteness. W. H. Freeman, San Francisco (1979)

    Google Scholar 

  5. Jansson, J.: Planar Minimum Weight Triangulations, Master’s Thesis, Department of Computer Science, Lund University, Sweden (1995)

    Google Scholar 

  6. Kucera, L.: Combinatorial Algorithms, SNTL, Publisher of Technical Literature (1989) ISBN 0-85274-298-3

    Google Scholar 

  7. Preparate, F.P., Shamos, M.I.: Computational Geometry - an Introduction. Springer, New York (1985)

    Google Scholar 

  8. Takaoka, T.: O(1) time algorithms for combinatorial generation by tree traversal. Computer Jurnal 42(5), 400–408 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Xiang, L., Ushijima, K.: On O(1) Time Algorithms for Combinatorial Generation. The Computer Journal 44(4), 292–302 (2001)

    Article  MATH  Google Scholar 

  10. Yang, B., T., Xu, Y., F., You, Z., Y.: A chain decomposition algorithm for the proof of a property on minimum weight triangulations (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of West Bohemia, Univerzitni 8, 306 14, Plzen, Czech Republic

    Tomas Hlavaty & Vaclav Skala

Authors
  1. Tomas Hlavaty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vaclav Skala
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hlavaty, T., Skala, V. (2004). Combinatories and Triangulations. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24767-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22057-2

  • Online ISBN: 978-3-540-24767-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation