Communications - Scientific Letters of the University of Zilina 2009, 11(3):39-42 | DOI: 10.26552/com.C.2009.3.39-42

Minimal Total Area Convex Set Partitioning Problem

Stefan Pesko1
1 Department of Mathematical Methods, Faculty of Management Science and Informatics, University of Zilina, Slovakia

The linear binary model for finding set partitioning of the points in the plane is studied.

We present heuristic which generates partitioning of points to clusters for a given number of seeds with searched seeds of clusters in a plane. For this cluster the convex hulls are constructed via Graham's scan algorithm. This approach is demonstrated on the real instance of Florida area with 235 points for 10 and 13 clusters.

Keywords: Convexity constraints, set partitioning problem, location problem, convex hull

Published: September 30, 2009  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Pesko, S. (2009). Minimal Total Area Convex Set Partitioning Problem. Communications - Scientific Letters of the University of Zilina, 11(3), 39-42. doi: 10.26552/com.C.2009.3.39-42
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. BERG, M.: Computational Geometry: Algorithms and Applications, 3rd rev. ed., Springer-Verlag, 2008, ISBN 978-3-540-77973-5, 386 pp. Go to original source...
    2. DALE, D., DROETTBOOM, M., FIRING, E., HUNTER, J.: Matplotlib, 2008, 754 pp.
    3. GHERMAN, D.: Recipe 66527: Finding the convex hull of a set of 2D points, http://code.activestate.com/recipes/66527/
    4. JANACEK, J., GABRISOVA, L.: Lagrangean Relaxation Based Approximate Approach to the Capacitated Location Problem. In: Scientific Letters of the University of Zilina, Communications 3, 2006, ISSN 1335-4205, pp. 19-24 Go to original source...
    5. JURICEK, M.: Private communication, Florida, USA
    6. KAUKIC, M.: Basics of Programming in Pylab (in Slovak), FEI TU Kosice, 2006, ISBN 80-8073-634-0, pp. 59
    7. MAKHORIN, A.: GNU Linear Programming Kit, Reference Manual, Version 4.29, Moscow, 2008, pp.154
    8. VAN ROSSUM, G., DRAKE, F.: Python Tutorial, Python Software Foundation, 2009, pp. 124

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content