Skip to main content
SpringerLink
Log in

Constrained Minimum-k-Star Clustering and its application to the consolidation of farmland

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

The present paper introduces and studies a new combinatorial clustering model for the consolidation of farmland. While the general problem turns out to be NP-hard even in quite restricted cases, the Size-restricted Minimum-k-Star Group Partition problem is solvable in polynomial time. Based on this tractability result, we derive a general approximation algorithm which, as the mathematical analysis and economic evaluation shows, performs well in theory and practice.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. We thank Dr. Paul Rintelen of the Bavarian State Institute for Agriculture for his support in the creation of these economic measures.

References

  • Brandes U, Gaertler M, Wagner D (2003) Experiments on graph clustering algorithms. Lecture notes in computer science, vol 2832/2003, pp 568–579. Springer, Berlin

  • Brieden A (2003) On the approximability of (discrete) convex maximization and its contribution to the consolidation of farmland. Habilitationsschrift. Tech. Univ., Munich

  • Brieden A, Gritzmann P (2004) A quadratic optimization model for the consolidation of farmland by means of lend-lease agreements. In: Ahr D, Fahrion R, Oswald M, Reinelt G (eds) Operations research proceedings 2003: selected papers of the international conference on operations research (OR 2003). Springer, Heidelberg, pp 324–331

  • Brieden A, Gritzmann P (2006) Von Ackerbau und polytopalen Halbnormen: Diskrete Optimierung für die Landwirtschaft. In: Hußmann S, Lutz-Westphal B (eds) Mathematik erleben—Kombinatorische Optimierung lehren und lernen. Vieweg Verlag, Wiesbaden

  • Elsner U (1997) Graph partitioning—a survey. Tech. Rep. 97–27. Tech. Univ., Chemnitz

  • Ghoulia-Houri A (1962) Caracterisation des matrices totalement unimodulaires. C R Acad Sci de Paris 254:1192–1194

    Google Scholar 

  • Guttmann-Beck N, Hassin R (1998) Approximation algorithms for min-sum p-clustering. Discre Appl Math 89:125–142

    Article  Google Scholar 

  • Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum Press, New York, pp 85–103

  • Orponen P, Mannila H (1987) On approximation preserving reductions: complete problems and robust measures. Technical Report C-1987-28, Department of Computer Science, University of Helsinki

  • Ostrovsky R, Rabani Y (2000) Polynomial time approximation schemes for geometric-k-clustering. IEEE Symp Found Comput Sci 41:349–358

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, 80290, Munich, Germany

    Steffen Borgwardt & Peter Gritzmann

  2. Universität der Bundeswehr München, 85579, Neubiberg, Germany

    Andreas Brieden

Authors
  1. Steffen Borgwardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Brieden
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Gritzmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Brieden.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borgwardt, S., Brieden, A. & Gritzmann, P. Constrained Minimum-k-Star Clustering and its application to the consolidation of farmland. Oper Res Int J 11, 1–17 (2011). https://doi.org/10.1007/s12351-009-0041-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-009-0041-y

Keywords

Mathematical Subject Classification (2000)

Search

Navigation