Document Open Access Logo

The PACE 2019 Parameterized Algorithms and Computational Experiments Challenge: The Fourth Iteration (Invited Paper)

Authors M. Ayaz Dzulfikar, Johannes K. Fichte , Markus Hecher



PDF
Thumbnail PDF

File

LIPIcs.IPEC.2019.25.pdf
  • Filesize: 0.88 MB
  • 23 pages

Document Identifiers

Author Details

M. Ayaz Dzulfikar
  • University of Indonesia, Kota Depok, Jawa Barat 16424, Indonesia
Johannes K. Fichte
  • Faculty of Computer Science, TU Dresden, 01062 Dresden, Germany
Markus Hecher
  • Institute of Logic and Computation, TU Wien, Favoritenstraße 9-11, 1040 Wien, Austria
  • University of Potsdam, Germany

Acknowledgements

The PACE challenge was supported by Networks [Networks project. https://www.thenetworkcenter.nl, 2019.], an NWO Gravitation project of the University of Amsterdam, Eindhoven University of Technology, Leiden University and the Center for Mathematics and Computer Science (CWI), by the Centre for Information and High Performance Computing (ZIH) of TU Dresden [Centre for Information Services and High Performance Computing. https://tu-dresden.de/zih/hochleistungsrechnen/, 2019. Project: pacechallage2019.], and by data-experts [data experts gmbh. https://www.data-experts.de/]. The prize money (4,000 EUR) was given through the generosity of Networks and data experts. We are grateful to Szymon Wasik and Jan Badura for the fruitful collaboration and for hosting the challenge at optil.io [Wasik et al., 2016]. We like to acknowledge the generous support by the High Performance Computing Center at TU Dresden, who gave us access to the HRSK-II and 80.000 CPU hours from February on to select instances and validate the results [Centre for Information Services and High Performance Computing. https://tu-dresden.de/zih/hochleistungsrechnen/, 2019. Project: pacechallage2019.].

Cite AsGet BibTex

M. Ayaz Dzulfikar, Johannes K. Fichte, and Markus Hecher. The PACE 2019 Parameterized Algorithms and Computational Experiments Challenge: The Fourth Iteration (Invited Paper). In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 25:1-25:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.IPEC.2019.25

Abstract

The organizers of the 4th Parameterized Algorithms and Computational Experiments challenge (PACE 2019) report on the 4th iteration of the PACE challenge. This year, the first track featured the MinVertexCover problem, which asks given an undirected graph G=(V,E) to output a set S subseteq V of vertices such that for every edge vw in E at least one endpoint belongs to S. The exact decision version of this problem is one of the most discussed problem if not even the prototypical problem in parameterized complexity theory. Another two tracks were dedicated to computing the hypertree width of a given hypergraph, which is a certain generalization of tree decompositions to hypergraphs that has widely been applied to problems in databases, constraint programming, and artificial intelligence. On one track we asked for submissions that compute hypertree decompositions of minimum width (MinHypertreeWidth) and on the other track we asked to heuristically compute hypertree decompositions of small width quickly (HeurHypertreeWidth). We received 28 implementations from 26 teams. This year we asked participants to submit solver descriptions in order to count as a submission for the challenge. We received those from 16 teams with overall 33 participants from 10 countries. One team submitted successful solutions to all three tracks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Complexity theory and logic
  • Mathematics of computing → Solvers
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Hypergraphs
Keywords
  • Parameterized Algorithms
  • Vertex Cover Problem
  • Hypertree Decompositions
  • Implementation Challenge
  • FPT

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. data experts gmbh. URL: https://www.data-experts.de/.
  2. Intelregistered Xeonregistered processor E5-2695 v3. https://ark.intel.com/content/www/us/en/ark/products/81057/intel-xeon-processor-e5-2695-v3-35m-cache-2-30-ghz.html, 2014.
  3. Centre for Information Services and High Performance Computing. https://tu-dresden.de/zih/hochleistungsrechnen/, 2019. Project: pacechallage2019.
  4. DIMACS Challenge. http://dimacs.rutgers.edu/programs/challenge/, 2019.
  5. Networks project. https://www.thenetworkcenter.nl, 2019.
  6. Mahmoud Abo Khamis, Hung Q. Ngo, Christopher Ré, and Atri Rudra. Joins via Geometric Resolutions: Worst-case and Beyond. In Proceedings of the 34th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS'15), pages 213-228, Melbourne, Victoria, Australia, 2015. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/2745754.2745776.
  7. Mahmoud Abo Khamis, Hung Q. Ngo, and Atri Rudra. FAQ: Questions Asked Frequently. In Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS '16), pages 13-28, San Francisco, California, USA, 2016. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/2902251.2902280.
  8. Michael Abseher, Nysret Musliu, and Stefan Woltran. htd - A Free, Open-Source Framework for (Customized) Tree Decompositions and Beyond. In Domenico Salvagnin and Michele Lombardi, editors, Proceedings of the 14th International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming (CPAIOR'17), volume 10335 of Lecture Notes in Computer Science, pages 376-386, Padova, Italy, June 2017. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-59776-8_30.
  9. Vasily Alferov. Cheburashka Vertex Cover solver. Zenodo, June 2019. URL: https://doi.org/10.5281/zenodo.3236897.
  10. Mario Alviano, Francesco Calimeri, Günther Charwat, Minh Dao-Tran, Carmine Dodaro, Giovambattista Ianni, Thomas Krennwallner, Martin Kronegger, Johannes Oetsch, Andreas Pfandler, Jörg Pührer, Christoph Redl, Francesco Ricca, Patrik Schneider, Martin Schwengerer, LaraKatharina Spendier, Johannes Peter Wallner, and Guohui Xiao. The Fourth Answer Set Programming Competition: Preliminary Report. In Pedro Cabalar and TranCao Son, editors, Proceedings of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'13), volume 8148 of Lecture Notes in Computer Science, pages 42-53. Springer Verlag, Corunna, Spain, September 2013. URL: https://doi.org/10.1007/978-3-642-40564-8_5.
  11. Krzysztof Apt. Principles of Constraint Programming. Cambridge University Press, Cambridge, New York, NY, USA, 1st edition, 2009. Google Scholar
  12. Molham Aref, Balder ten Cate, Todd J. Green, Benny Kimelfeld, Dan Olteanu, Emir Pasalic, Todd L. Veldhuizen, and Geoffrey Washburn. Design and Implementation of the LogicBlox System. In Susan B. Davidson and Zack Ives, editors, Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data (SIGMOD'15), pages 1371-1382, Melbourne, Victoria, Australia, 2015. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/2723372.2742796.
  13. Patricia C. Arocena, Boris Glavic, Radu Ciucanu, and Renée J. Miller. The iBench Integration Metadata Generator. In Chen Li and Volker Markl, editors, Proceedings of Very Large Data Bases (VLDB) Endowment, volume 9:3, pages 108-119. Very Large Data Base Endowment, November 2015. URL: https://github.com/RJMillerLab/ibench.
  14. G. Audemard, F. Boussemart, C. Lecoutre, and C. Piette. XCSP3: an XML-based format designed to represent combinatorial constrained problems. http://xcsp.org, 2016.
  15. Nurzhan Bakibayev, Tomáš Kočiský, Dan Olteanu, and Jakub Závodný. Aggregation and Ordering in Factorised Databases. Proceedings of Very Large Data Bases Endowment (VLDB'13), 6(14):1990-2001, September 2013. URL: https://doi.org/10.14778/2556549.2556579.
  16. Max Bannach and Sebastian Berndt. Practical Access to Dynamic Programming on Tree Decompositions. In Yossi Azar, Hannah Bast, and Grzegorz Herman, editors, Proceedings of the 26th Annual European Symposium on Algorithms (ESA 2018), volume 112 of Leibniz International Proceedings in Informatics (LIPIcs), pages 6:1-6:13, Helsinki, Finland, 2018. Dagstuhl Publishing. URL: https://doi.org/10.4230/LIPIcs.ESA.2018.6.
  17. Max Bannach, Sebastian Berndt, and Thorsten Ehlers. Jdrasil: A Modular Library for Computing Tree Decompositions. In Costas S. Iliopoulos, Solon P. Pissis, Simon J. Puglisi, and Rajeev Raman, editors, Proceedings of the 16th International Symposium on Experimental Algorithms (SEA 2017), volume 75 of Dagstuhl Publishing, pages 28:1-28:21, London, UK, 2017. Leibniz International Proceedings in Informatics (LIPIcs). URL: https://doi.org/10.4230/LIPIcs.SEA.2017.28.
  18. Michael Benedikt, George Konstantinidis, Giansalvatore Mecca, Boris Motik, Paolo Papotti, Donatello Santoro, and Efthymia Tsamoura. Benchmarking the Chase. In Floris Geerts, editor, Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS'17), pages 37-52, Chicago, Illinois, USA, 2017. Assoc. Comput. Mach., New York. URL: https://github.com/dbunibas/chasebench.
  19. J. Berg, N. Lodha, M. Järvisalo, and S. Szeider. MaxSAT benchmarks based on determining generalized hypertree-width. Technical report, MaxSAT Evaluation 2017, 2017. Google Scholar
  20. Sebastian Berndt. Computing Tree Width: From Theory to Practice and Back. In Florin Manea, Russell G. Miller, and Dirk Nowotka, editors, Sailing Routes in the World of Computation: Proceedings of the 14th Conference on Computability in Europe (CiE 2018), volume 10936 of Lecture Notes in Computer Science, pages 81-88, Kiel, Germany, 2018. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-94418-0_8.
  21. Manuel Bichler, Michael Morak, and Stefan Woltran. Single-shot Epistemic Logic Program Solving. In Jeffrey S. Rosenschein and Jérôme Lang, editors, Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI 2018), pages 1714-1720. The AAAI Press, 2018. Google Scholar
  22. Johannes Blum and Sabine Storandt. Computation and Growth of Road Network Dimensions. In Lusheng Wang and Daming Zhu, editors, Proceedings of the 24th International Computing and Combinatorics Conference (COCOON 2018), volume 10976 of Lecture Notes in Computer Science, pages 230-241, Qing Dao, China, July 2018. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-94776-1_20.
  23. Jori Bomanson, Martin Gebser, and Tomi Janhunen. Improving the Normalization of Weight Rules in Answer Set Programs. In Eduardo Fermé and João Leite, editors, Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA'14), pages 166-180, Funchal, Madeira, Portugal, September 2014. Springer Verlag. Google Scholar
  24. Jori Bomanson, Martin Gebser, and Tomi Janhunen. LP2NORMAL and LP2NORMAL2. https://research.ics.aalto.fi/software/asp/lp2normal/, 2016.
  25. John A. Bondy and U. Murty. Graph theory, volume 244 of Graduate Texts in Mathematics. Springer Verlag, 2008. Google Scholar
  26. Édouard Bonnet and Florian Sikora. The PACE 2018 Parameterized Algorithms and Computational Experiments Challenge: The Third Iteration. In Christophe Paul and Michal Pilipczuk, editors, Proceedings of the 13th International Symposium on Parameterized and Exact Computation (IPEC 2018), volume 115 of Leibniz International Proceedings in Informatics (LIPIcs), pages 26:1-26:15, Helsinki, Finland, 2019. Dagstuhl Publishing. URL: https://doi.org/10.4230/LIPIcs.IPEC.2018.26.
  27. G. Brewka, T. Eiter, and M. Truszczyński. Answer set programming at a glance. Communications of the ACM, 54(12):92-103, 2011. URL: https://doi.org/10.1145/2043174.2043195.
  28. Shaowei Cai, Wenying Hou, Jinkun Lin, and Yuanjie Li. Improving Local Search for Minimum Weight Vertex Cover by Dynamic Strategies. In IJCAI, pages 1412-1418. ijcai.org, 2018. Google Scholar
  29. Francesco Calimeri, Giovambattista Ianni, and Francesco Ricca. The third open answer set programming competition. Theory Pract. Log. Program., 14:117-135, January 2014. URL: https://doi.org/10.1017/S1471068412000105.
  30. Francesco Calimeri, Simona Perri, and Jessica Zangari. Optimizing Answer Set Computation via Heuristic-Based Decomposition. Theory Pract. Log. Program., 19(4):603 - -628, 2019. URL: https://doi.org/10.1017/S1471068419000036.
  31. Mathieu Chapelle, Mathieu Liedloff, Ioan Todinca, and Yngve Villanger. Treewidth and Pathwidth parameterized by the vertex cover number. Discrete Applied Mathematics, 216:114-129, 2017. Google Scholar
  32. Günther Charwat and Stefan Woltran. Dynamic Programming-based QBF Solving. In Florian Lonsing and Martina Seidl, editors, Proceedings of the 4th International Workshop on Quantified Boolean Formulas (QBF'16), volume 1719, pages 27-40. CEUR Workshop Proceedings (CEUR-WS.org), 2016. co-located with 19th International Conference on Theory and Applications of Satisfiability Testing (SAT'16). Google Scholar
  33. Günther Charwat and Stefan Woltran. Expansion-based QBF Solving on Tree Decompositions. Fundam. Inform., 167(1-2):59-92, 2019. Google Scholar
  34. Jiehua Chen and Sven Grottke. A fast solver for Minimum Vertex Cover. Zenodo, June 2019. URL: https://doi.org/10.5281/zenodo.3236992.
  35. David Cohen, Peter Jeavons, and Marc Gyssens. A unified theory of structural tractability for constraint satisfaction problems. J. of Computer and System Sciences, 74(5):721-743, 2008. Google Scholar
  36. Christophe Crespelle, Eduard Eiben, and Kirill Simonov. Vertex Cover Solver for PACE 2019. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3235533.
  37. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  38. Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, and Krzysztof Sornat. Approximation and Parameterized Complexity of Minimax Approval Voting. J. Artif. Intell. Res., 63:495-513, 2018. URL: https://doi.org/10.1613/jair.1.11253.
  39. Rina Dechter. Constraint Processing. Morgan Kaufmann, 2003. Google Scholar
  40. 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 Jiong Guo and Danny Hermelin, editors, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016), volume 63 of Leibniz International Proceedings in Informatics (LIPIcs), pages 30:1-30:9, Aarhus, Denmark, 2017. Dagstuhl Publishing. URL: https://doi.org/10.4230/LIPIcs.IPEC.2016.30.
  41. Holger Dell, Christian Komusiewicz, Nimrod Talmon, and Mathias Weller. The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration. In Daniel Lokshtanov and Naomi Nishimura, editors, Proceedings of the 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), volume 89 of Leibniz International Proceedings in Informatics (LIPIcs), pages 30:1-30:12, Vienna, Austria, 2018. Dagstuhl Publishing. URL: https://doi.org/10.4230/LIPIcs.IPEC.2017.30.
  42. Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson. The Shortest Path Problem: Ninth DIMACS Implementation Challenge. http://users.diag.uniroma1.it/challenge9/download.shtml, 2009.
  43. Marc Denecker, Joost Vennekens, Stephen Bond, Martin Gebser, and Mirosław Truszczyński. The Second Answer Set Programming Competition. In Esra Erdem, Fangzhen Lin, and Torsten Schaub, editors, Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'09), volume 5753 of Lecture Notes in Computer Science, pages 637-654. Springer Verlag, Potsdam, Germany, September 2009. URL: https://doi.org/10.1007/978-3-642-04238-6_75.
  44. Artan Dermaku, Tobias Ganzow, Georg Gottlob, Ben McMahan, Nysret Musliu, and Marko Samer. Heuristic Methods for Hypertree Decomposition. In Alexander Gelbukh and Eduardo F. Morales, editors, Procedings of the 7th Mexican International Conference on Artificial Intelligence on Advances in Artificial Intelligence (MICAI 2008), volume 5317 of Lecture Notes in Computer Science, pages 1-11. Springer Verlag, 2008. URL: https://doi.org/10.1007/978-3-540-88636-5_1.
  45. Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate Texts in Mathematics. Springer Verlag, 2012. Google Scholar
  46. Diego Delle Donne and Guido Tagliavini. Star Routing: Between Vehicle Routing and Vertex Cover. In COCOA, volume 11346 of Lecture Notes in Computer Science, pages 522-536. Springer, 2018. Google Scholar
  47. Eugene F. Dumitrescu, Allison L. Fisher, Timothy D. Goodrich, Travis S. Humble, Blair D. Sullivan, and Andrew L. Wright. Benchmarking treewidth as a practical component of tensor network simulations. PLOS ONE, 13(12):1-19, December 2018. URL: https://doi.org/10.1371/journal.pone.0207827.
  48. Arnaud Durand and Stefan Mengel. Structural tractability of counting of solutions to conjunctive queries. Theoretical Computer Science, 57(4):1202-1249, 2015. Google Scholar
  49. M. Ayaz Dzulfikar, Johannes K. Fichte, and Markus Hecher. daajoe/sat2vc - A CNF-SAT to VC converter, 2019. URL: https://github.com/daajoe/sat2vc.
  50. M. Ayaz Dzulfikar, Johannes K. Fichte, and Markus Hecher. PACE2019: Track 1 - vertex cover instances. Zenodo, July 2019. URL: https://doi.org/10.5281/zenodo.3354609.
  51. Leah Epstein, Asaf Levin, and Gerhard J. Woeginger. Vertex Cover Meets Scheduling. Algorithmica, 74(3):1148-1173, 2016. Google Scholar
  52. Michael R. Fellows, Lars Jaffke, Aliz Izabella Király, Frances A. Rosamond, and Mathias Weller. What Is Known About Vertex Cover Kernelization? In Adventures Between Lower Bounds and Higher Altitudes, volume 11011 of Lecture Notes in Computer Science, pages 330-356. Springer, 2018. Google Scholar
  53. J. K. Fichte. daajoe/gtfs2graphs - A GTFS transit feed to Graph Format Converter, 2016. URL: https://github.com/daajoe/gtfs2graphs.
  54. Johannes K. Fichte. ASP Horn Backdoors. https://github.com/daajoe/asp_horn_backdoors, 2014.
  55. Johannes K. Fichte. SAT Horn Backdoors. https://github.com/daajoe/sat_horn_backdoors, 2018.
  56. Johannes K. Fichte and Markus Hecher. PACE2019: Track 2a+b - hypertree decomposition instances. Zenodo, July 2019. URL: https://doi.org/10.5281/zenodo.3354607.
  57. Johannes K. Fichte, Markus Hecher, Neha Lodha, and Stefan Szeider. An SMT Approach to Fractional Hypertree Width. In John Hooker, editor, Proceedings of the 24th International Conference on Principles and Practice of Constraint Programming (CP 2018), volume 11008 of Lecture Notes in Computer Science, pages 109-127, Lille, France, 2018. Springer Verlag. Google Scholar
  58. Johannes K. Fichte, Markus Hecher, Michael Morak, and Stefan Woltran. Answer Set Solving with Bounded Treewidth Revisited. In Marcello Balduccini and Tomi Janhunen, editors, Proceedings of the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'17), volume 10377 of Lecture Notes in Computer Science, pages 132-145, Espoo, Finland, July 2017. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-61660-5_13.
  59. Johannes K. Fichte, Markus Hecher, Michael Morak, and Stefan Woltran. DynASP2.5: Dynamic programming on tree decompositions in action. In Daniel Lokshtanov and Naomi Nishimura, editors, Proceedings of the 12th International Symposium on Parameterized and Exact Computation (IPEC'17). Dagstuhl Publishing, 2017. URL: https://doi.org/10.4230/LIPIcs.IPEC.2017.17.
  60. Johannes K. Fichte, Markus Hecher, Michael Morak, and Stefan Woltran. Exploiting Treewidth for Projected Model Counting and its Limits. In Olaf Beyersdorff and Christoph M. Wintersteiger, editors, Proceedings on the 21th International Conference on Theory and Applications of Satisfiability Testing (SAT'18), volume 10929 of Lecture Notes in Computer Science, pages 165-184, Oxford, UK, July 2018. Springer Verlag. Google Scholar
  61. Johannes K. Fichte, Markus Hecher, and Markus Zisser. gpusat2 - An Improved GPU Model Counter. In Simon de Givry and Thomas Schiex, editors, Proceedings of the 25th International Conference on Principles and Practice of Constraint Programming (CP 2018), 2019. To appear. Google Scholar
  62. Johannes K. Fichte, Neha Lodha, and Stefan Szeider. SAT-Based Local Improvement for Finding Tree Decompositions of Small Width. In Serge Gaspers and Toby Walsh, editors, Proceedings of the 20th International Conference on Theory and Applications of Satisfiability Testing (SAT 2017), volume 10491 of Lecture Notes in Computer Science, pages 401-411, Melbourne, VIC, Australia, 2017. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-66263-3_25.
  63. Johannes K. Fichte and Stefan Szeider. Backdoors to Tractable Answer-Set Programming. Artificial Intelligence, 220(0):64-103, 2015. URL: https://doi.org/10.1016/j.artint.2014.12.001.
  64. Johannes Klaus Fichte and Markus Hecher. Treewidth and Counting Projected Answer Sets. In Marcello Balduccini, Yuliya Lierler, and Stefan Woltran, editors, Proceedings of the 15th International Conference on Logic Programming and Nonmonotonic Reasoning LPNMR 2019, volume 11481 of Lecture Notes in Computer Science, pages 105-119, Philadelphia, PA, USA, 2019. Springer Verlag. URL: https://doi.org/10.1007/978-3-030-20528-7_9.
  65. Johannes Klaus Fichte, Markus Hecher, and Arne Meier. Counting Complexity for Reasoning in Abstract Argumentation. In Pascal Van Hentenryck and Zhi-Hua Zhou, editors, Proceedings of the 33rd AAAI Conference on Artificial Intelligence, AAAI 2019, pages 2827-2834, Honolulu, Hawaii, USA, 2019. The AAAI Press. Google Scholar
  66. Johannes Klaus Fichte, Markus Hecher, Stefan Woltran, and Markus Zisser. Weighted Model Counting on the GPU by Exploiting Small Treewidth. In Yossi Azar, Hannah Bast, and Grzegorz Herman, editors, Proceedings of the 26th Annual European Symposium on Algorithms (ESA'18), volume 112 of Leibniz International Proceedings in Informatics (LIPIcs), pages 28:1-28:16. Dagstuhl Publishing, 2018. URL: https://doi.org/10.4230/LIPIcs.ESA.2018.28.
  67. Aleksander Figiel. An exact vertex cover solver using kernels. Zenodo, June 2019. URL: https://doi.org/10.5281/zenodo.3236867.
  68. Wolfgang Fischl, Georg Gottlob, Davide M. Longo, and Reinhard Pichler. HyperBench: a benchmark of hypergraphs. http://hyperbench.dbai.tuwien.ac.at, 2017.
  69. Wolfgang Fischl, Georg Gottlob, Davide Mario Longo, and Reinhard Pichler. HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings. In Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS'19), pages 464-480, Amsterdam, Netherlands, 2019. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/3294052.3319683.
  70. Wolfgang Fischl, Georg Gottlob, and Reinhard Pichler. General and Fractional Hypertree Decompositions: Hard and Easy Cases. In Jan Van den Bussche and Marcelo Arenas, editors, Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS'18), pages 17-32, Houston, TX, USA, June 2018. Assoc. Comput. Mach., New York. Google Scholar
  71. Daniel Fremont. counting-benchmarks. http://tinyurl.com/countingbenchmarks, 2016.
  72. Eugene C. Freuder. A sufficient condition for backtrack-bounded search. J. of the ACM, 29(1):24-32, 1982. Google Scholar
  73. Marco Gario. Backdoors for SAT. Master’s thesis, TU Dresden, 2011. Program sources at URL: https://marco.gario.org/work/master/.
  74. Marco Gario. HornVCBuilder. https://marco.gario.org/work/master/, 2011.
  75. Marco Gario. Horn backdoor detection via Vertex Cover: Benchmark Description. In Adrian Balint, Anton Belov, Daniel Diepold, Simon Gerber, Matti Järvisalo, and Carsten Sinz, editors, Proceedings of SAT Challenge 2012; Solver and Benchmark Descriptions, Helsinki, Finland, 2012. University of Helsinki. Google Scholar
  76. Serge Gaspers, Joachim Gudmundsson, Mitchell Jones, Julián Mestre, and Stefan Rümmele. Turbocharging Treewidth Heuristics. In Jiong Guo and Danny Hermelin, editors, Proceedings of the 11th International Symposium on Parameterized and Exact Computation (IPEC'16), volume 63 of Leibniz International Proceedings in Informatics (LIPIcs), pages 13:1-13:13. Dagstuhl Publishing, 2017. URL: https://doi.org/10.4230/LIPIcs.IPEC.2016.13.
  77. M. Gebser, T. Schaub, S. Thiele, and P. Veber. Detecting Inconsistencies in Large Biological Networks with Answer Set Programming. Theory Pract. Log. Program., 11(2-3):323-360, 2011. Google Scholar
  78. Martin Gebser, Roland Kaminski, Benjamin Kaufmann, and Torsten Schaub. Clingo = ASP + Control: Preliminary Report. CoRR, abs/1405.3694, 2014. URL: http://arxiv.org/abs/1405.3694.
  79. Martin Gebser, Lengning Liu, Gayathri Namasivayam, André Neumann, Torsten Schaub, and Mirosław Truszczyński. The First Answer Set Programming System Competition. In Chitta Baral, Gerhard Brewka, and John Schlipf, editors, Proceedings of the 9th Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'07), volume 4483 of Lecture Notes in Computer Science, pages 3-17, Tempe, AZ, USA, May 2007. Springer Verlag. URL: https://doi.org/10.1007/978-3-540-72200-7_3.
  80. F. Geerts, G. Mecca, P. Papotti, and D. Santoro. Mapping and cleaning. In Isabel Cruz, Elena Ferrari, and Yufei Tao, editors, Proceedings of the IEEE 30th International Conference on Data Engineering (ICDE'14), pages 232-243, March 2014. Google Scholar
  81. Martin Josef Geiger. Implementation of a Metaheuristic for the Steiner Tree Problem in Graphs. Medeley Data, 2018. URL: https://doi.org/10.17632/yf9vpkgwdr.1.
  82. G. Gottlob, N. Leone, and F. Scarcello. Hypertree Decompositions and Tractable Queries. J. of Computer and System Sciences, 64(3):579-627, 2002. Google Scholar
  83. Georg Gottlob, Gianluigi Greco, and Francesco Scarcello. Treewidth and Hypertree Width, pages 3 - -38. Cambridge University Press, Cambridge, 2014. URL: https://doi.org/10.1017/CBO9781139177801.002.
  84. Georg Gottlob, Zoltan Miklos, Nysret Musliu, and Marko Samer. Hypertree Complementary Approaches to Constraint Satisfaction, 2016. URL: https://www.dbai.tuwien.ac.at/proj/hypertree/downloads.html.
  85. Georg Gottlob and Marko Samer. A Backtracking-based Algorithm for Hypertree Decomposition. J. of Experimental Algorithmics, 13:1:1.1-1:1.19, February 2009. Google Scholar
  86. Martin Grohe and Dániel Marx. Constraint Solving via Fractional Edge Covers. In Proceedings of the of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), pages 289-298. ACM Press, 2006. Google Scholar
  87. Martin Grohe and Dániel Marx. Constraint solving via fractional edge covers. ACM Transactions on Algorithms, 11(1):Art. 4, 20, 2014. Google Scholar
  88. Yuanbo Guo, Zhengxiang Pan, and Jeff Heflin. LUBM: A benchmark for OWL knowledge base systems. Web Semantics: Science, Services and Agents on the World Wide Web, 3(2):158-182, 2005. Google Scholar
  89. LLC Gurobi Optimization. Gurobi Optimizer Reference Manual, 2019. URL: http://www.gurobi.com.
  90. Michael Hamann and Ben Strasser. Graph Bisection with Pareto Optimization. J. of Experimental Algorithmics, 23:1.2:1-1.2:34, February 2018. URL: https://doi.org/10.1145/3173045.
  91. Falko Hegerfeld and Florian Nelles. hubhegnel/pace-2019: Release for zenodo. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3234674.
  92. Demian Hespe, Sebastian Lamm, Christian Schulz, and Darren Strash. WeGotYouCovered, May 2019. URL: https://doi.org/10.5281/zenodo.2816116.
  93. Demian Hespe, Sebastian Lamm, Christian Schulz, and Darren Strash. WeGotYouCovered: The winning solver from the PACE 2019 implementation challenge, vertex cover track. CoRR, 2019. URL: http://arxiv.org/abs/1908.06795.
  94. Marijn J. H. Heule, Matti Juhani Järvisalo, and Martin Suda, editors. Proceedings of the SAT Competition 2018: Solver and Benchmark Descriptions, volume B. Department of Computer Science, University of Helsinki, University of Helsinki, 2018. Google Scholar
  95. Holger H. Hoos and Thomas Stützle. SATLIB: An online resource for research on SAT. In Ian P. Gent, Hans van Maaren, and Toby Walsh, editors, Proceedings of the 3rd Workshop on Satisfiability (SAT'00), pages 283-292, Renesse, The Netherlands, 2000. IOS Press. SATLIB is available online at URL: www.satlib.org.
  96. Md. Rafiqul Islam, Imran Hossain Arif, and Rifat Hasan Shuvo. Generalized vertex cover using chemical reaction optimization. Appl. Intell., 49(7):2546-2566, 2019. Google Scholar
  97. Yoichi Iwata. Linear-Time Kernelization for Feedback Vertex Set. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), volume 80 of Leibniz International Proceedings in Informatics (LIPIcs), pages 68:1-68:14. Dagstuhl Publishing, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.68.
  98. Yoichi Iwata and Yusuke Kobayashi. Improved Analysis of Highest-Degree Branching for Feedback Vertex Set. CoRR, abs/1905.12233, 2019. URL: http://arxiv.org/abs/1905.12233.
  99. Yoichi Iwata and Takuto Shigemura. Separator-Based Pruned Dynamic Programming for Steiner Tree. In AAAI, pages 1520-1527. AAAI Press, 2019. Google Scholar
  100. T. Janhunen and I. Niemelä. The Answer Set Programming Paradigm. AI Magazine, 37(3):13-24, 2016. URL: https://doi.org/10.1609/aimag.v37i3.2671.
  101. P. Jégou, H. Kanso, and C. Terrioux. On the Relevance of Optimal Tree Decompositions for Constraint Networks. In Proceedings of the IEEE 30th International Conference on Tools with Artificial Intelligence (ICTAI 2018), pages 738-743. IEEE Computer Soc., November 2018. URL: https://doi.org/10.1109/ICTAI.2018.00116.
  102. Roland Kaminski. clingo - A grounder and solver for logic programs. https://github.com/potassco/clingo, 2019.
  103. Kustaa Kangas, Mikko Koivisto, and Sami Salonen. A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions. In Christophe Paul and Michal Pilipczuk, editors, Proceedings of the 13th International Symposium on Parameterized and Exact Computation (IPEC 2018), volume 115 of Leibniz International Proceedings in Informatics (LIPIcs), pages 5:1-5:13. Dagstuhl Publishing, 2019. URL: https://doi.org/10.4230/LIPIcs.IPEC.2018.5.
  104. Richard M. Karp. Reducibility Among Combinatorial Problems. In Complexity of Computer Computations, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972. Google Scholar
  105. Steven Kelk, Georgios Stamoulis, and Taoyang Wu. Treewidth distance on phylogenetic trees. Theoretical Computer Science, 731:99-117, 2018. URL: https://doi.org/10.1016/j.tcs.2018.04.004.
  106. Mahmoud Abo Khamis, Hung Q. Ngo, and Atri Rudra. FAQ: questions asked frequently. CoRR, abs/1504.04044, 2017. Google Scholar
  107. Krzysztof Kiljan and Marcin Pilipczuk. Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set. In Gianlorenzo D'Angelo, editor, Proceedings of the 17th International Symposium on Experimental Algorithms (SEA 2018), volume 103 of Leibniz International Proceedings in Informatics (LIPIcs), pages 12:1-12:12. Dagstuhl Publishing, 2018. URL: https://doi.org/10.4230/LIPIcs.SEA.2018.12.
  108. Daphne Koller and Nir Friedman. Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning. MIT Press, 2009. Google Scholar
  109. Tuukka Korhonen, Jeremias Berg, and Matti Järvisalo. Enumerating Potential Maximal Cliques via SAT and ASP. In Thomas Eiter and Sarit Kraus, editors, Proceedings of the International Joint Conference on Artificial Intelligence IJCAI 2019, Macao, China, 2019. The AAAI Press. Google Scholar
  110. Tuukka Korhonen, Jeremias Berg, and Matti Järvisalo. Solving Graph Problems via Potential Maximal Cliques: An Experimental Evaluation of the Bouchitté-Todinca Algorithm. J. of Experimental Algorithmics, 24(1):1.9:1-1.9:19, February 2019. URL: https://doi.org/10.1145/3301297.
  111. Philipp Klaus Krause, Lukas Larisch, and Felix Salfelder. The tree-width of C. Discr. Appl. Math., 2019. URL: https://doi.org/10.1016/j.dam.2019.01.027.
  112. R. Krithika, Diptapriyo Majumdar, and Venkatesh Raman. Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels. Theory Comput. Syst., 62(8):1690-1714, 2018. Google Scholar
  113. Srijan Kumar, Bryan Hooi, Disha Makhija, Mohit Kumar, Christos Faloutsos, and VS Subrahmanian. Rev2: Fraudulent user prediction in rating platforms. In Yi Chang and Yan Liu, editors, Proceedings of the 11th ACM International Conference on Web Search and Data Mining (WSDM'18), pages 333-341, Marina Del Rey, CA, USA, 2018. Assoc. Comput. Mach., New York. Google Scholar
  114. Srijan Kumar, Francesca Spezzano, VS Subrahmanian, and Christos Faloutsos. Edge weight prediction in weighted signed networks. In Francesco Bonchi and Josep Domingo-Ferrer, editors, Proceedings of the IEEE 16th International Conference on Data Mining (ICDM'16), pages 221-230, Barcelona, Catalonia, Spain, 2016. IEEE Computer Soc. Google Scholar
  115. Hung V. Le. Structural Results and Approximation Algorithms in Minor-free Graphs. PhD thesis, Oregon State University, 2018. URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/d217qv924.
  116. Viktor Leis, Andrey Gubichev, Atanas Mirchev, Peter Boncz, Alfons Kemper, and Thomas Neumann. How Good Are Query Optimizers, Really? Proceedings of Very Large Data Bases (VLDB) Endowment, 9(3):204-215, November 2015. Google Scholar
  117. Jure Leskovec. Stanford Network Analysis Project. https://snap.stanford.edu, 2009.
  118. Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Predicting Positive and Negative Links in Online Social Networks. In Proceedings of the 19th International Conference on World Wide Web (WWW '10), pages 641-650, New York, NY, USA, 2010. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/1772690.1772756.
  119. Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Signed Networks in Social Media. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI '10), pages 1361-1370, New York, NY, USA, 2010. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/1753326.1753532.
  120. Jure Leskovec, Jon Kleinberg, and Christos Faloutsos. Graph Evolution: Densification and Shrinking Diameters. ACM Trans. Knowl. Discov. Data, 1(1), March 2007. URL: https://doi.org/10.1145/1217299.1217301.
  121. Zijie Li and Peter van Beek. Finding Small Backdoors in SAT Instances. In Canadian Conference on AI, volume 6657 of Lecture Notes in Computer Science, pages 269-280. Springer, 2011. Google Scholar
  122. Cong Han Lim and Stephen Wright. k-Support and Ordered Weighted Sparsity for Overlapping Groups: Hardness and Algorithms. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Proceedings of Advances in Neural Information Processing Systems 30 (NIPS 2017), pages 284-292. Curran Associates, Inc., 2017. Google Scholar
  123. Neha Lodha, Sebastian Ordyniak, and Stefan Szeider. SAT-Encodings for Special Treewidth and Pathwidth. In Serge Gaspers and Toby Walsh, editors, Proceedings of the 20th International Conference on Theory and Applications of Satisfiability Testing (SAT 2017), volume 10491 of Lecture Notes in Computer Science, pages 429-445, Melbourne, VIC, Australia, 2017. Springer Verlag. URL: https://doi.org/10.1007/978-3-319-66263-3_27.
  124. Davide Mario Longo. Pace2019 Hypertree Width Exact. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3236358.
  125. Davide Mario Longo. Pace2019 Hypertree Width Heuristic. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3236369.
  126. Diptapriyo Majumdar, Venkatesh Raman, and Saket Saurabh. Polynomial Kernels for Vertex Cover Parameterized by Small Degree Modulators. Theory Comput. Syst., 62(8):1910-1951, 2018. Google Scholar
  127. Silviu Maniu, Pierre Senellart, and Suraj Jog. An Experimental Study of the Treewidth of Real-World Graph Data. In Pablo Barcelo and Marco Calautti, editors, Proceedings of the 22nd International Conference on Database Theory (ICDT 2019), volume 127 of Leibniz International Proceedings in Informatics (LIPIcs), pages 12:1-12:18. Dagstuhl Publishing, 2019. URL: https://doi.org/10.4230/LIPIcs.ICDT.2019.12.
  128. Marco Maratea, Francesco Ricca, Wolfgang Faber, and Nicola Leone. Look-back techniques and heuristics in DLV: Implementation, evaluation, and comparison to QBF solvers. J. Algorithms, 63(1-3):70-89, 2008. Benchmarks can be found at http://asparagus.cs.uni-potsdam.de/contest/downloads/benchmarks-score-dlp.tgz. URL: https://doi.org/10.1016/j.jalgor.2008.02.006.
  129. Thorsten Ehlers Max Bannach, Sebastian Berndt and Dirk Nowotka. SAT-Encodings of Tree Decompositions. In Marijn Heule, Matti Juhani Järvisalo, and Martin Suda, editors, Proceedings of SAT Competition 2018: Solver and Benchmark Descriptions, number Report B-2018-1 in B, page 72. University of Helsinki, Department of Computer Science, 2018. Google Scholar
  130. Julian McAuley and Jure Leskovec. Learning to Discover Social Circles in Ego Networks. In Proceedings of the 25th International Conference on Neural Information Processing Systems (NIPS'12), pages 539-547, USA, 2012. Curran Associates Inc. Google Scholar
  131. Naomi Nishimura, Prabhakar Ragde, and Stefan Szeider. Solving #SAT using vertex covers. Acta Informatica, 44(7-8):509-523, 2007. Google Scholar
  132. Dan Olteanu and Jakub Závodný. Size Bounds for Factorised Representations of Query Results. ACM Trans. Database Syst., 40(1):2:1-2:44, March 2015. URL: https://doi.org/10.1145/2656335.
  133. Steven Prestwich. CNF Encodings. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfiability, chapter 2, pages 75-97. IOS Press, 2009. Google Scholar
  134. Noam Ravid, Dori Medini, and Benny Kimelfeld. Ranked Enumeration of Minimal Triangulations. In Dan Suciu and Christoph Koch, editors, Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS 2019), pages 74-88, Amsterdam, Netherlands, 2019. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/3294052.3319678.
  135. Matei Ripeanu, Adriana Iamnitchi, and Ian Foster. Mapping the Gnutella Network. IEEE Internet Computing, 6(1):50-57, January 2002. URL: https://doi.org/10.1109/4236.978369.
  136. Neil Robertson and P.D. Seymour. Graph Minors. II. Algorithmic Aspects of Tree-Width. J. Algorithms, 7(3):309-322, 1986. Google Scholar
  137. Marko Samer and Stefan Szeider. Backdoor Trees. In AAAI, pages 363-368. AAAI Press, 2008. Google Scholar
  138. Marko Samer and Stefan Szeider. Fixed-Parameter Tractability. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfiability, chapter 13, pages 425-454. IOS Press, 2009. Google Scholar
  139. André Schidler and Stefan Szeider. HtdSMT - An SMT based solver for hypertree decompositions. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3236333.
  140. C. Sinz, A. Kaiser, and W. Küchlin. Formal methods for the validation of automotive product configuration data. AI EDAM, 17(01):75-97, 2003. URL: http://www-sr.informatik.uni-tuebingen.de/~sinz/DC.
  141. Ben Strasser. Road Graphs as Tree-Decomposition PACE Test Instances, 2016. URL: https://github.com/ben-strasser/road-graphs-pace16.
  142. Ben Strasser. Computing Tree Decompositions with FlowCutter: PACE 2017 Submission. CoRR, abs/1709.08949, 2017. URL: http://arxiv.org/abs/1709.08949.
  143. Hisao Tamaki. Positive-Instance Driven Dynamic Programming for Treewidth. In Kirk Pruhs and Christian Sohler, editors, Proceedings of the 25th Annual European Symposium on Algorithms (ESA 2017), volume 87 of Leibniz International Proceedings in Informatics (LIPIcs), pages 68:1-68:13, Vienna, Austria, 2017. Dagstuhl Publishing. URL: https://doi.org/10.4230/LIPIcs.ESA.2017.68.
  144. Hisao Tamaki. Positive-instance driven dynamic programming for treewidth. J. Comb. Optim., 37(4):1283-1311, May 2019. URL: https://doi.org/10.1007/s10878-018-0353-z.
  145. Transaction Processing Performance Council (TPC). TPC-H decision support benchmark. Technical report, TPC, 2014. URL: http://www.tpc.org/tpch/default.asp.
  146. James Trimble. jamestrimble/heidi: v1.0.0: Pace Challenge 2019 version. Zenodo, June 2019. URL: https://doi.org/10.5281/zenodo.3237427.
  147. James Trimble. jamestrimble/hypebeast: v1.0.0: PACE Challenge 2019 version. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3082314.
  148. James Trimble. jamestrimble/peaty: v1.0.0: PACE Challenge 2019 entry. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3082356.
  149. Edward Tsang. Foundations of Constraint Satisfaction. Academic Press, 1993. Google Scholar
  150. René van Bevern, Till Fluschnik, and Oxana Yu. Tsidulko. Parameterized algorithms and data reduction for safe convoy routing. CoRR, abs/1806.09540, 2018. URL: http://arxiv.org/abs/1806.09540.
  151. Tom C. van der Zanden and Hans L. Bodlaender. Computing Treewidth on the GPU. In Daniel Lokshtanov and Naomi Nishimura, editors, Proceedings of the 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), volume 89 of Leibniz International Proceedings in Informatics (LIPIcs), pages 29:1-29:13, Vienna, Austria, 2018. dp. URL: https://doi.org/10.4230/LIPIcs.IPEC.2017.29.
  152. Tom Cornelis van der Zanden. Theory and Practical Applications of Treewidth. PhD thesis, Utrecht University, 2019. Google Scholar
  153. Rim van Wersch and Steven Kelk. ToTo: An open database for computation, storage and retrieval of tree decompositions. Discr. Appl. Math., 217:389-393, 2017. URL: https://doi.org/10.1016/j.dam.2016.09.023.
  154. Szymon Wasik, Maciej Antczak, Jan Badura, Artur Laskowski, and Tomasz Sternal. Optil.Io: Cloud Based Platform For Solving Optimization Problems Using Crowdsourcing Approach. In Eric Gilbert and Karrie Karahalios, editors, Proceedings of the 19th ACM Conference on Computer Supported Cooperative Work and Social Computing Companion, CSCW '16 Companion, pages 433-436, New York, NY, USA, 2016. Assoc. Comput. Mach., New York. URL: https://doi.org/10.1145/2818052.2869098.
  155. Ke Xu. BHOSLIB: Benchmarks with Hidden Optimum Solutions for Graph Problems (Maximum Clique, Maximum Independent Set, Minimum Vertex Cover and Vertex Coloring). http://sites.nlsde.buaa.edu.cn/~kexu/benchmarks/graph-benchmarks.htm, 2014.
  156. Bogdan Zavalnij and Sandor Szabo. zbogdan/pace-2019 a. Zenodo, May 2019. URL: https://doi.org/10.5281/zenodo.3228802.
  157. Yuting Zhao and Fangzhen Lin. Answer Set Programming Phase Transition: A Study on Randomly Generated Programs. In Catuscia Palamidessi, editor, Proceedings of the 19th International Conference on Logic Programming (ICLP'03), volume 2916 of Lecture Notes in Computer Science, pages 239-253, Mumbai, India, December 2003. Springer Verlag. URL: https://doi.org/10.1007/978-3-540-24599-5_17.
  158. Michal Ziobro and Marcin Pilipczuk. Finding Hamiltonian Cycle in Graphs of Bounded Treewidth: Experimental Evaluation. CoRR, abs/1803.00927, 2018. URL: http://arxiv.org/abs/1803.00927.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail