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Finding Hamiltonian Cycle in Graphs of Bounded Treewidth: Experimental Evaluation

Authors Michal Ziobro, Marcin Pilipczuk

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Michal Ziobro
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Marcin Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland

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Michal Ziobro and Marcin Pilipczuk. Finding Hamiltonian Cycle in Graphs of Bounded Treewidth: Experimental Evaluation. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 29:1-29:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in graphs of bounded treewidth: graphs that can be sweeped with separators of bounded size. These efficient algorithms usually follow the dynamic programming paradigm. In the recent years, we have seen a rapid and quite unexpected development of involved techniques for solving various computational problems in graphs of bounded treewidth. One of the most surprising directions is the development of algorithms for connectivity problems that have only single-exponential dependency (i.e., 2^{{O}(t)}) on the treewidth in the running time bound, as opposed to slightly superexponential (i.e., 2^{{O}(t log t)}) stemming from more naive approaches. In this work, we perform a thorough experimental evaluation of these approaches in the context of one of the most classic connectivity problem, namely Hamiltonian Cycle.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Dynamic programming
  • Empirical Evaluation of Algorithms
  • Treewidth
  • Hamiltonian Cycle


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  1. Recent trends in kernelization: theory and experimental evaluation - project website, 2018. URL:
  2. Richard Bellman. Combinatorial processes and dynamic programming. Technical report, RAND CORP SANTA MONICA CA, 1958. Google Scholar
  3. Andreas Bjorklund. Determinant sums for undirected hamiltonicity. In Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on, pages 173-182. IEEE, 2010. Google Scholar
  4. Andreas Björklund, Thore Husfeldt, Petteri Kaski, and Mikko Koivisto. Trimmed moebius inversion and graphs of bounded degree. Theory of Computing Systems, 47(3):637-654, 2010. Google Scholar
  5. Andreas Björklund, Petteri Kaski, Lukasz Kowalik, and Juho Lauri. Engineering motif search for large graphs. In 2015 Proceedings of the Seventeenth Workshop on Algorithm Engineering and Experiments (ALENEX), pages 104-118. SIAM, 2014. Google Scholar
  6. Hans L. Bodlaender, Marek Cygan, Stefan Kratsch, and Jesper Nederlof. Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth. Inf. Comput., 243:86-111, 2015. URL:
  7. Hajo Broersma, Fedor V Fomin, Pim van’t Hof, and Daniël Paulusma. Fast exact algorithms for hamiltonicity in claw-free graphs. In International Workshop on Graph-Theoretic Concepts in Computer Science, pages 44-53. Springer, 2009. Google Scholar
  8. Marek Cygan, Fedor V Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  9. Marek Cygan, Stefan Kratsch, and Jesper Nederlof. Fast hamiltonicity checking via bases of perfect matchings. In Proceedings of the forty-fifth annual ACM symposium on Theory of computing, pages 301-310. ACM, 2013. Google Scholar
  10. Marek Cygan, Jesper Nederlof, Marcin Pilipczuk, Michal Pilipczuk, Joham MM van Rooij, and Jakub Onufry Wojtaszczyk. Solving connectivity problems parameterized by treewidth in single exponential time. In Foundations of Computer Science (FOCS), 2011 IEEE 52nd Annual Symposium on, pages 150-159. IEEE, 2011. Google Scholar
  11. Holger Dell, Thore Husfeldt, Bart MP Jansen, Petteri Kaski, Christian Komusiewicz, and Frances A Rosamond. The first parameterized algorithms and computational experiments challenge. In LIPIcs-Leibniz International Proceedings in Informatics, volume 63. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  12. Holger Dell, Christian Komusiewicz, Nimrod Talmon, and Mathias Weller. The pace 2017 parameterized algorithms and computational experiments challenge: The second iteration. Google Scholar
  13. Stefan Fafianie, Hans L Bodlaender, and Jesper Nederlof. Speeding up dynamic programming with representative sets: an experimental evaluation of algorithms for steiner tree on tree decompositions. Algorithmica, 71(3):636-660, 2015. Google Scholar
  14. Serge Gaspers, Joachim Gudmundsson, Mitchell Jones, Julián Mestre, and Stefan Rümmele. Turbocharging treewidth heuristics. In Jiong Guo and Danny Hermelin, editors, 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, August 24-26, 2016, Aarhus, Denmark, volume 63 of LIPIcs, pages 13:1-13:13. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL:
  15. M. Haythorpe. FHCP challenge set, 2015. Google Scholar
  16. Michael Held and Richard M Karp. A dynamic programming approach to sequencing problems. Journal of the Society for Industrial and Applied Mathematics, 10(1):196-210, 1962. Google Scholar
  17. Daniel Lokshtanov, Dániel Marx, and Saket Saurabh. Known algorithms on graphs on bounded treewidth are probably optimal. In Dana Randall, editor, Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23-25, 2011, pages 777-789. SIAM, 2011. URL:
  18. Daniel Lokshtanov, Dániel Marx, and Saket Saurabh. Slightly superexponential parameterized problems. In Dana Randall, editor, Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23-25, 2011, pages 760-776. SIAM, 2011. URL:
  19. Ketan Mulmuley, Umesh V. Vazirani, and Vijay V. Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7(1):105-113, 1987. URL:
  20. Neil Robertson and Paul D Seymour. Graph minors. III. Planar tree-width. Journal of Combinatorial Theory, Series B, 36(1):49-64, 1984. Google Scholar
  21. Ben Strasser. Computing tree decompositions with flowcutter: PACE 2017 submission. CoRR, abs/1709.08949, 2017. URL:
  22. Johan M. M. van Rooij, Hans L. Bodlaender, and Peter Rossmanith. Dynamic programming on tree decompositions using generalised fast subset convolution. In Amos Fiat and Peter Sanders, editors, Algorithms - ESA 2009, 17th Annual European Symposium, Copenhagen, Denmark, September 7-9, 2009. Proceedings, volume 5757 of Lecture Notes in Computer Science, pages 566-577. Springer, 2009. URL:
  23. Michał Ziobro and Marcin Pilipczuk. Finding Hamiltonian Cycle in graphs of bounded treewidth: Experimental evaluation. code repository, 2018. Google Scholar
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