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Voluntary Land Exchange in Forests - Project Arborchange


People: Dr. Steffen Borgwardt
Partners: Bayerische Staatsministerium für Ernährung, Landwirtschaft und Forsten, Bayerische Forstverwaltung, Dr. Stefan Schaffner, Holger Hastreiter
Period: R&D project Arborchange April 2012 - July 2013, transition into regular use of the Staatsministerium and Forstverwaltung 2013 - today



The voluntary land exchange of forest lots owners is a new tool to improve on problems in the cost-effective structure of forest regions owned by private owners. Some of the methods for land consolidation are helpful, but there are many new challenges to overcome in forestry regions, like an extreme numbers of different owners, badly shaped lots, and a difficult to implement process in practice.

For these reasons, the Bayerische Staatsministerium für Ernährung, Landwirtschaft und Forsten and the Bayerische Forstverwaltung initiated the R&D project ST 280 Arborchange for the division of mathematical methods and the implementation of software to support voluntary land exchange processes on several levels. This R&D project was lead by Dr. Steffen Borgwardt, and the cooperation with the Staatsministerium was coordinated by Dr. Stefan Schaffner.

Core parts of this project concerned the selection of key owners in forest regions that provide a large potential for improvement when taking part. This can be modelled as a weighted dense k-subgraph problem, which is known to be NP-hard and difficult to approximate when a graph does not satisfy the triangle inequality. The underlying graphs of this application, on the other hand, exhibit a special structure, for which this question can be solved favorably in practice.

Further key aspects were the division of economic measures for the structural problems of these regions. These are used to choose regions where a land exchange is initiated, and tell us about the individual advantages or disadvantages of owners in a virtually planned land exchange.

The results of this research were implemented as modules Arboreval and Arboropt for the base tool Arborchange - the whole package is called Arbortec. A manual is found here.

Selected Publications

  • S. Borgwardt, F. Schmiedl (2014) Threshold-based preprocessing for approximating the dense k-subgraph problem. European Journal of Operational Research 234, pp. 631-640
  • S. Borgwardt, S. Schaffner, M. Suda (2014) Geometrische Kennzahlen für die forstfachliche Bewertung der Zersplitterung von Privatwaldregionen. Manuscript, submitted
  • S. Borgwardt (2013) Das Programm Arbortec - Arborchange mit Arboreval und Arboropt. Softwarebericht und Handbuch für die Entwicklungsarbeiten des Projekts ST 280 - Arborchange

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.