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Jdrasil: A Modular Library for Computing Tree Decompositions

Authors Max Bannach, Sebastian Berndt, Thorsten Ehlers

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Max Bannach
Sebastian Berndt
Thorsten Ehlers

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Max Bannach, Sebastian Berndt, and Thorsten Ehlers. Jdrasil: A Modular Library for Computing Tree Decompositions. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 28:1-28:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


While the theoretical aspects concerning the computation of tree width - one of the most important graph parameters - are well understood, it is not clear how it can be computed practically. We present the open source Java library Jdrasil that implements several different state of the art algorithms for this task. By experimentally comparing these algorithms, we show that the default choices made in Jdrasil lead to an competitive implementation (it took the third place in the first PACE challenge) while also being easy to use and easy to extend.
  • tree width
  • algorithmic library
  • experimental evaluation


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  1. Stefan Arnborg, Derek G. Corneil, and Andrzej Proskurowski. Complexity of Finding Embeddings in a k-Tree. SIAM J. Algebraic Discrete Methods, 8(2):277-284, 1987. URL:
  2. Stefan Arnborg and Andrzej Proskurowski. Linear Time Algorithms for NP-hard Problems Restricted to Partial k-Trees. Discrete applied mathematics, 23(1):11-24, 1989. URL:
  3. Gilles Audemard and Laurent Simon. Predicting Learnt Clauses Quality in Modern SAT Solvers. In Proc. IJCAI, pages 399-404, 2009. Google Scholar
  4. Olivier Bailleux and Yacine Boufkhad. Efficient CNF Encoding of Boolean Cardinality Constraints. In Proc. CP, pages 108-122. Springer, 2003. URL:
  5. Max Bannach, Sebastian Berndt, and Thorsten Ehlers. Jdrasil, 2016. URL:
  6. Alessandro Berarducci and Benedetto Intrigila. On the Cop Number of a Graph. Advances in Applied Mathematics, 14(4):389-403, 1993. URL:
  7. Jeremias Berg and Matti Järvisalo. SAT-Based Approaches to Treewidth Computation: An Evaluation. In Proc. ICTAI, pages 328-335. IEEE Computer Society, 2014. URL:
  8. Armin Biere. Lingeling, Plingeling, Picosat and Precosat at SAT Race 2010. FMV Report Series Technical Report, 10(1), 2010. Google Scholar
  9. Hans L. Bodlaender. A Linear Time Algorithm for Finding Tree-Decompositions of Small Treewidth. In Proc. STOC, pages 226-234. ACM, 1993. URL:
  10. Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, and Danny Hermelin. On Problems Without Polynomial Kernels. Journal of Computer and System Sciences, 75(8):423-434, 2009. URL:
  11. Hans L. Bodlaender, Pal Gronas Drange, Markus S. Dregi, Fedor V. Fomin, Daniel Lokshtanov, and Michal Pilipczuk. An O(c^k n) 5-Approximation Algorithm for Treewidth. In Proc. FOCS, pages 499-508, Oct 2013. URL:
  12. Hans L. Bodlaender, Fedor V. Fomin, Arie M. C. A. Koster, Dieter Kratsch, and Dimitrios M. Thilikos. On Exact Algorithms for Treewidth. ACM Trans. Algorithms, 9(1):12:1-12:23, 2012. URL:
  13. Hans L. Bodlaender, Bart M. P. Jansen, and Stefan Kratsch. Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization. In Proc. ICALP, volume 6755 of Lecture Notes in Computer Science, pages 437-448. Springer, 2011. URL:
  14. Hans L. Bodlaender and Arie M. C. A. Koster. Treewidth Computations I. Upper bounds. Information and Computation, 208(3):259-275, 2010. URL:
  15. Hans L. Bodlaender and Arie M. C. A. Koster. Treewidth computations II. Lower Bounds. Information and Computation, 209(7):1103-1119, 2011. URL:
  16. Hans L. Bodlaender, Arie M. C. A. Koster, and Frank van den Eijkhof. Pre-Processing for Triangulation of Probabilistic Networks. Computational Intelligence, 21(3):286-305, 2005. URL:
  17. Hans L. Bodlaender and Tom van der Zanden. BZTreewidth, 2016. URL:
  18. Liming Cai, Jianer Chen, Rodney G. Downey, and Michael R. Fellows. Advice Classes of Parameterized Tractability. Ann. Pure Appl. Logic, 84(1):119-138, 1997. URL:
  19. Bruno Courcelle. Graph Rewriting: An Algebraic and Logic Approach. In Formal Models and Semantics, volume B of Handbook of Theoretical Computer Science, pages 193-242. Elsevier, Amsterdam, Netherlands and MIT Press, Cambridge, Massachusetts, 1990. URL:
  20. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer Publishing Company, Incorporated, 1st edition, 2015. Google Scholar
  21. Holger Dell, Thore Husfeldt, Bart M. P. Jansen, Petteri Kaski, Christian Komusiewicz, and Frances A. Rosamond. The First Parameterized Algorithms and Computational Experiments Challenge. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016), volume 63 of LIPIcs, pages 30:1-30:9. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL:
  22. DIMACS Graph Format. Accessed: 2017-01-26. URL:
  23. Niklas Eén and Niklas Sörensson. An Extensible SAT-Solver. In Proc. SAT, volume 2919 of Lecture Notes in Computer Science, pages 502-518. Springer, 2003. URL:
  24. Vibhav Gogate and Rina Dechter. A Complete Anytime Algorithm for Treewidth. In Proc. UAI, pages 201-208. AUAI Press, 2004. Google Scholar
  25. Thore Husfeldt and Iyad A. Kanj, editors. Proc. IPEC, volume 43 of LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2015. Google Scholar
  26. IBM. IBM ILOG CPLEX Optimization Studio CPLEX User’s Manual. URL:
  27. David R. Karger and Nathan Srebro. Learning Markov Networks: Maximum Bounded Tree-Width Graphs. In Proc. SODA, pages 392-401. ACM/SIAM, 2001. Google Scholar
  28. The Parameterized Algorithms and Computational Experiments Challenge (PACE). Accessed: 2017-01-26. URL:
  29. Neil Robertson and Paul D. Seymour. Graph Minors. XIII. The Disjoint Paths Problem. Journal of Combinatorial Theory, 63(1):65-110, 1995. URL:
  30. Marko Samer and Helmut Veith. Encoding Treewidth into SAT. In Proc. SAT, volume 5584 of Lecture Notes in Computer Science, pages 45-50. Springer, 2009. URL:
  31. Paul D. Seymour and Robin Thomas. Graph Searching and a Min-Max Theorem for Tree-Width. Journal of Combinatorial Theory, Series B, 58(1):22-33, 1993. URL:
  32. Yinglei Song, Chunmei Liu, Russell L. Malmberg, Fangfang Pan, and Liming Cai. Tree Decomposition Based Fast Search of RNA Structures Including Pseudoknots in Genomes. In Proc. CSB, pages 223-234. IEEE Computer Society, 2005. Google Scholar
  33. Hisao Tamaki. Exact treewidth, 2016. URL:
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