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The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set

Authors Ernestine Großmann , Tobias Heuer , Christian Schulz , Darren Strash

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Author Details

Ernestine Großmann
  • Universität Heidelberg, Germany
Tobias Heuer
  • Karlsruhe Institute of Technology, Germany
Christian Schulz
  • Universität Heidelberg, Germany
Darren Strash
  • Hamilton College, Clinton, NY, USA

Funding

Partially supported by DFG grant SCHU 2567/3-1.

Acknowledgements

The PACE challenge was supported by Networks [Networks project, 2017]. The prize money (€4000) was generously provided by Networks [Networks project, 2017], an NWO Gravitation project of the University of Amsterdam, Eindhoven University of Technology, Leiden University and the Center for Mathematics and Computer Science (CWI). We are grateful to the whole optil.io team, led by Szymon Wasik, and especially to Jan Badura and Artur Laskowski for the fruitful collaboration and for hosting the competition at the optil.io online judge system.

Cite AsGet BibTex

Ernestine Großmann, Tobias Heuer, Christian Schulz, and Darren Strash. The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.IPEC.2022.26

Abstract

The Parameterized Algorithms and Computational Experiments challenge (PACE) 2022 was devoted to engineer algorithms solving the NP-hard Directed Feedback Vertex Set (DFVS) problem. The DFVS problem is to find a minimum subset X ⊆ V in a given directed graph G = (V,E) such that, when all vertices of X and their adjacent edges are deleted from G, the remainder is acyclic. Overall, the challenge had 90 participants from 26 teams, 12 countries, and 3 continents that submitted their implementations to this year’s competition. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Feedback Vertex Set
  • Algorithm Engineering
  • FPT
  • Kernelization
  • Heuristics

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References

  1. Networks project, 2017. URL: http://www.thenetworkcenter.nl.
  2. Faisal N. Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, and Darren Strash. Recent advances in practical data reduction. Special Issue of SPP Big Data, 2022. URL: http://arxiv.org/abs/2012.12594.
  3. N. Faisal Abu-Khzam, R. Michael Fellows, A. Michael Langston, and Henry W. Suters. Crown structures for vertex cover kernelization. Theory Comput. Syst., 41(3):411-430, 2007. URL: https://doi.org/10.1007/s00224-007-1328-0.
  4. Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Mount Doom - An Exact Solver for Directed Feedback Vertex Set, June 2022. URL: https://doi.org/10.5281/zenodo.6645235.
  5. Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Orodruin — A Heuristic Solver for Directed Feedback Vertex Set, June 2022. URL: https://doi.org/10.5281/zenodo.6645245.
  6. Andrei Arhire and Paul Diac. _UAIC_ANDREIARHIRE_ - A Heuristic Solver for the Directed Feedback Vertex Set Problem, June 2022. URL: https://doi.org/10.5281/zenodo.6646187.
  7. Albert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 286(5439):509-512, 1999. URL: https://doi.org/10.1126/science.286.5439.509.
  8. Timon Behr. Direfever, June 2022. URL: https://doi.org/10.5281/zenodo.6651761.
  9. Moritz Bergenthal, Jona Dirks, Thorben Freese, Jakob Gahde, and Enna Gerhard. GraPA-JAVA, June 2022. URL: https://doi.org/10.5281/zenodo.6647003.
  10. Benjamin Bergougnoux, Eduard Eiben, Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. Towards a polynomial kernel for directed feedback vertex set. Algorithmica, 83(5):1201-1221, 2021. URL: https://doi.org/10.1007/s00453-020-00777-5.
  11. Mert Biyikli. MertBiyikli/BreakingCycles: Fourth release, June 2022. URL: https://doi.org/10.5281/zenodo.6674065.
  12. Édouard Bonnet and Florian Sikora. The PACE 2018 parameterized algorithms and computational experiments challenge: The third iteration. In Christophe Paul and Michal Pilipczuk, editors, 13th International Symposium on Parameterized and Exact Computation, IPEC 2018, August 20-24, 2018, Helsinki, Finland, volume 115 of LIPIcs, pages 26:1-26:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.IPEC.2018.26.
  13. Maria Bresich, Günther Raidl, and Johannes Varga. HyMeHeu-solver - A Hybrid Metaheuristic Solver for the Directed Feedback Vertex Set Problem, June 2022. URL: https://doi.org/10.5281/zenodo.6643236.
  14. Shaowei Cai, Jinkun Lin, and Chuan Luo. Finding a small vertex cover in massive sparse graphs: Construct, local search, and preprocess. J. Artif. Intell. Res., 59:463-494, 2017. URL: https://doi.org/10.1613/jair.5443.
  15. Shaowei Cai, Kaile Su, Chuan Luo, and Abdul Sattar. NuMVC: An efficient local search algorithm for minimum vertex cover. J. Artif. Intell. Res., 46:687-716, 2013. URL: https://doi.org/10.1613/jair.3907.
  16. Daniel Castro. Daniel1993/pace-2022: pace-2022, June 2022. URL: https://doi.org/10.5281/zenodo.6634725.
  17. Jianer Chen, Yang Liu, Songjian Lu, Barry O'Sullivan, and Igor Razgon. A fixed-parameter algorithm for the directed feedback vertex set problem. J. ACM, 55(5):21:1-21:19, 2008. URL: https://doi.org/10.1145/1411509.1411511.
  18. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  19. Holger Dell, Henri Froese, Lukas Geis, Jonathan Guthermuth, Anselm Haak, Lars Huth, Frank Kammer, Marius Lotz, Johannes Meintrup, Timo Mertin, Manuel Penschuck, and Lukas Schwarz. BreakingTheCycle, June 2022. This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grants 379157101, ME 2088/5-1 (FOR 2975 — Algorithms, Dynamics, and Information Flow in Networks). URL: https://doi.org/10.5281/zenodo.6602946.
  20. 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, August 24-26, 2016, Aarhus, Denmark, volume 63 of LIPIcs, pages 30:1-30:9. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPIcs.IPEC.2016.30.
  21. 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, 12th International Symposium on Parameterized and Exact Computation, IPEC 2017, September 6-8, 2017, Vienna, Austria, volume 89 of LIPIcs, pages 30:1-30:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.IPEC.2017.30.
  22. Dickel, Miskovic, and Uhrmacher. pace-2022-dum, May 2022. URL: https://doi.org/10.5281/zenodo.6599645.
  23. Yuming Du, Qingyun Zhang, Junzhou Xu, Shungen Zhang, Chao Liao, Zhihuai Chen, Zhibo Sun, Zhouxing Su, Junwen Ding, Chen Wu, Pinyan Lu, and Zhipeng Lv. Huawei_tcs_dfvs_solver, June 2022. URL: https://doi.org/10.5281/zenodo.6638370.
  24. M. Ayaz Dzulfikar, Johannes Klaus Fichte, and Markus Hecher. The PACE 2019 parameterized algorithms and computational experiments challenge: The fourth iteration (invited paper). In Bart M. P. Jansen and Jan Arne Telle, editors, 14th International Symposium on Parameterized and Exact Computation, IPEC 2019, September 11-13, 2019, Munich, Germany, volume 148 of LIPIcs, pages 25:1-25:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.IPEC.2019.25.
  25. John D Eblen, Charles A Phillips, Gary L Rogers, and Michael A Langston. The maximum clique enumeration problem: algorithms, applications, and implementations. In BMC Bioinformatics, volume 13, page S5, 2012. URL: https://doi.org/10.1186/1471-2105-13-S10-S5.
  26. Paul Erdős and Alfréd Rényi. On Random Graphs I. Publicationes Mathematicae (Debrecen), 6:290-297, 1959 1959. Google Scholar
  27. Guy Even, Joseph Naor, Baruch Schieber, and Madhu Sudan. Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica, 20(2):151-174, 1998. URL: https://doi.org/10.1007/PL00009191.
  28. Florian. fsikora/pace22: First version for pace, June 2022. URL: https://doi.org/10.5281/zenodo.6624196.
  29. Fedor V. Fomin, Serge Gaspers, Daniel Lokshtanov, and Saket Saurabh. Exact algorithms via monotone local search. J. ACM, 66(2), March 2019. URL: https://doi.org/10.1145/3284176.
  30. Daniel Funke, Sebastian Lamm, Ulrich Meyer, Manuel Penschuck, Peter Sanders, Christian Schulz, Darren Strash, and Moritz von Looz. Communication-free massively distributed graph generation. J. Parallel Distributed Comput., 131:200-217, 2019. URL: https://doi.org/10.1016/j.jpdc.2019.03.011.
  31. Bathie Gabriel, Berthe Gaétan, Coudert-Osmont Yoann, Desobry David, Reinald Amadeus, and Rocton Mathis. Dreyfvs, June 2022. URL: https://doi.org/10.5281/zenodo.6638217.
  32. Philippe Galinier, Eunice Adjarath Lemamou, and Mohamed Wassim Bouzidi. Applying local search to the feedback vertex set problem. J. Heuristics, 19(5):797-818, 2013. URL: https://doi.org/10.1007/s10732-013-9224-z.
  33. Georges Gardarin and Stefano Spaccapietra. Integrity of data bases: A general lockout algorithm with deadlock avoidance. In G. M. Nijssen, editor, Modelling in Data Base Management Systems, Proceeding of the IFIP Working Conference on Modelling in Data Base Management Systems, Freudenstadt, Germany, January 5-8, 1976, pages 395-412. North-Holland, 1976. Google Scholar
  34. Serge Gaspers and Matthias Mnich. Feedback vertex sets in tournaments. J. Graph Theory, 72(1):72-89, 2013. URL: https://doi.org/10.1002/jgt.21631.
  35. E. N. Gilbert. Random graphs. Ann. Math. Statist., 30(4):1141-1144, December 1959. URL: https://doi.org/10.1214/aoms/1177706098.
  36. Luca Gugelmann, Konstantinos Panagiotou, and Ueli Peter. Random hyperbolic graphs: Degree sequence and clustering. In Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part II, volume 7392 of Lecture Notes in Computer Science, pages 573-585. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-31585-5_51.
  37. Venkatesan Guruswami, Johan HÅstad, Rajsekar Manokaran, Prasad Raghavendra, and Moses Charikar. Beating the random ordering is hard: Every ordering CSP is approximation resistant. SIAM Journal on Computing, 40(3):878-914, 2011. URL: https://doi.org/10.1137/090756144.
  38. Venkatesan Guruswami and Euiwoong Lee. Simple proof of hardness of feedback vertex set. Theory Comput., 12(1):1-11, 2016. URL: https://doi.org/10.4086/toc.2016.v012a006.
  39. Ruben Götz. Ruben Bachelor Thesis, June 2022. URL: https://doi.org/10.5281/zenodo.6604728.
  40. Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash. Finding all global minimum cuts in practice. In Proc. ESA 2020, volume 173 of Leibniz Int. Proc. Informatics, pages 59:1-59:20, 2020. URL: https://doi.org/10.4230/LIPIcs.ESA.2020.59.
  41. Demian Hespe, Sebastian Lamm, Christian Schulz, and Darren Strash. WeGotYouCovered: The winning solver from the PACE 2019 challenge, vertex cover track. In H. Martin Bücker, Xiaoye Sherry Li, and Sivasankaran Rajamanickam, editors, Proceedings of the SIAM Workshop on Combinatorial Scientific Computing, CSC 2020, Seattle, USA, February 11-13, 2020, pages 1-11. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611976229.1.
  42. A. Itai, A. G. Konheim, and M. Rodeh. A sparse table implementation of priority queues. In S. Even and O. Kariv, editors, Proceedings of the 8th Colloquium on Automata, Languages and Programming, volume 115 of LNCS, pages 417-431. Springer, 1981. URL: https://doi.org/10.1007/3-540-10843-2_34.
  43. Aman Jain, Sachin Agarwal, Nimish Agrawal, Soumyajit Karmakar, and Srinibas Swain. DRIP: Directed feedback vertex set computation using Reductions and Integer Programming, June 2022. URL: https://doi.org/10.5281/zenodo.6618812.
  44. Aman Jain, Sachin Agarwal, Nimish Agrawal, Soumyajit Karmakar, and Srinibas Swain. FEDRER: Feedback vertex set using Edge Density and REmove Redundant, June 2022. URL: https://doi.org/10.5281/zenodo.6618777.
  45. Arthur B. Kahn. Topological Sorting of Large Networks. Commun. ACM, 5(11):558-562, 1962. URL: https://doi.org/10.1145/368996.369025.
  46. Richard M. Karp. Reducibility among combinatorial problems. In Raymond E. Miller and James W. Thatcher, editors, Proceedings of a symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972. URL: https://doi.org/10.1007/978-1-4684-2001-2_9.
  47. Leon Kellerhals, Tomohiro Koana, André Nichterlein, and Philipp Zschoche. The PACE 2021 parameterized algorithms and computational experiments challenge: Cluster editing. In Petr A. Golovach and Meirav Zehavi, editors, 16th International Symposium on Parameterized and Exact Computation, IPEC 2021, September 8-10, 2021, Lisbon, Portugal, volume 214 of LIPIcs, pages 26:1-26:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.IPEC.2021.26.
  48. Rafael Kiesel and Andre Schidler. DAGger - An Exact Directed Feedback Vertex Set Solver, June 2022. URL: https://doi.org/10.5281/zenodo.6627405.
  49. Tomasz Kociumaka and Marcin Pilipczuk. Faster deterministic feedback vertex set. Information Processing Letters, 114(10):556-560, 2014. URL: https://doi.org/10.1016/j.ipl.2014.05.001.
  50. Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche. Data reduction for maximum matching on real-world graphs: Theory and experiments. In Proc. ESA 2018, volume 112 of Leibniz Int. Proc. Informatics, pages 53:1-53:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ESA.2018.53.
  51. Lukasz Kowalik, Marcin Mucha, Wojciech Nadara, Marcin Pilipczuk, Manuel Sorge, and Piotr Wygocki. The PACE 2020 parameterized algorithms and computational experiments challenge: Treedepth. In Yixin Cao and Marcin Pilipczuk, editors, 15th International Symposium on Parameterized and Exact Computation, IPEC 2020, December 14-18, 2020, Hong Kong, China (Virtual Conference), volume 180 of LIPIcs, pages 37:1-37:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.IPEC.2020.37.
  52. Dmitri V. Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, and Marián Boguñá. Hyperbolic geometry of complex networks. CoRR, abs/1006.5169, 2010. URL: http://arxiv.org/abs/1006.5169.
  53. Kenneth Langedal. KennethLangedal/DFVS: pace-2022, June 2022. URL: https://doi.org/10.5281/zenodo.6630611.
  54. Charles E. Leiserson and James B. Saxe. Retiming synchronous circuitry. Algorithmica, 6(1):5-35, 1991. URL: https://doi.org/10.1007/BF01759032.
  55. Mile Lemaic. Markov-Chain-Based Heuristics for the Feedback Vertex Set Problem for Digraph. PhD thesis, University of Cologne, 2008. URL: http://kups.ub.uni-koeln.de/id/eprint/2547.
  56. Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, June 2014.
  57. Orna Lichtenstein and Amir Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In Mary S. Van Deusen, Zvi Galil, and Brian K. Reid, editors, Conference Record of the Twelfth Annual ACM Symposium on Principles of Programming Languages, New Orleans, Louisiana, USA, January 1985, pages 97-107. ACM Press, 1985. URL: https://doi.org/10.1145/318593.318622.
  58. Hen-Ming Lin and Jing-Yang Jou. On Computing the Minimum Feedback Vertex Set of a Directed Graph by Contraction Operations. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 19(3):295-307, 2000. URL: https://doi.org/10.1109/43.833199.
  59. Daniel Lokshtanov, Pranabendu Misra, Joydeep Mukherjee, Fahad Panolan, Geevarghese Philip, and Saket Saurabh. 2-approximating feedback vertex set in tournaments. ACM Trans. Algorithms, 17(2), April 2021. URL: https://doi.org/10.1145/3446969.
  60. Daniel Lokshtanov, M. S. Ramanuajn, and Saket Saurabh. When recursion is better than iteration: A linear-time algorithm for acyclicity with few error vertices. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '18, pages 1916-1933, USA, 2018. Society for Industrial and Applied Mathematics. URL: https://doi.org/10.1137/1.9781611975031.125.
  61. Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Roohani Sharma, and Meirav Zehavi. Wannabe bounded treewidth graphs admit a polynomial kernel for DFVS. In Zachary Friggstad, Jörg-Rüdiger Sack, and Mohammad R. Salavatipour, editors, Algorithms and Data Structures - 16th International Symposium, WADS 2019, Edmonton, AB, Canada, August 5-7, 2019, Proceedings, volume 11646 of Lecture Notes in Computer Science, pages 523-537. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-24766-9_38.
  62. Alex Meiburg. Reduction Rules and ILP Are All You Need: Minimal Directed Feedback Vertex Set, 2022. URL: https://doi.org/10.48550/ARXIV.2208.01119.
  63. Alexander Meiburg. PACE 2022 - DFVS-Via-Flattening Solver (DVFS), June 2022. Derived from https://github.com/Timeroot/DVFS_PACE 2022/tree/pace-2022. URL: https://doi.org/10.5281/zenodo.6650921.
  64. Yosuke Mizutani. PACE 2022 - Exact, June 2022. URL: https://doi.org/10.5281/zenodo.6604875.
  65. Mathew Penrose. Random geometric graphs. Number 5 in Oxford Studies in Probability. Oxford University Press, 2003. Google Scholar
  66. Manuel Penschuck, Ulrik Brandes, Michael Hamann, Sebastian Lamm, Ulrich Meyer, Ilya Safro, Peter Sanders, and Christian Schulz. Recent advances in scalable network generation. CoRR, abs/2003.00736, 2020. URL: http://arxiv.org/abs/2003.00736.
  67. Rick Plachetta and Alexander van der Grinten. SAT-and-reduce for vertex cover: Accelerating branch-and-reduce by SAT solving. In Martin Farach-Colton and Sabine Storandt, editors, Proceedings of the Symposium on Algorithm Engineering and Experiments, ALENEX 2021, Virtual Conference, January 10-11, 2021, pages 169-180. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976472.13.
  68. U. N. Raghavan, R. Albert, and S. Kumara. Near Linear Time Algorithm to Detect Community Structures in Large-Scale Networks. Physical Review E, 76(3), 2007. URL: https://doi.org/10.1103/PhysRevE.76.036106.
  69. Igor Razgon. Computing minimum directed feedback vertex set in O^*(1.9977ⁿ). In Giuseppe F. Italiano, Eugenio Moggi, and Luigi Laura, editors, Theoretical Computer Science, 10th Italian Conference, ICTCS 2007, Rome, Italy, October 3-5, 2007, Proceedings, pages 70-81. World Scientific, 2007. URL: https://doi.org/10.1142/9789812770998_0010.
  70. Ewald Speckenmeyer. On Feedback Problems in Digraphs. In Graph-Theoretic Concepts in Computer Science, 15th International Workshop, WG '89, Castle Rolduc, The Netherlands, June 14-16, 1989, Proceedings. Springer, 1989. URL: https://doi.org/10.1007/3-540-52292-1_16.
  71. Leon Stichternath, Ozan Heydt, Kenneth Dietrich, and Philipp Haker. Grapa-Rust, June 2022. URL: https://doi.org/10.5281/zenodo.6603799.
  72. Sylwester Swat. swacisko/pace-2022: First release of DiVerSeS, a solver for the Directed Feedback Vertex Set problem, June 2022. URL: https://doi.org/10.5281/zenodo.6643144.
  73. Stefan Tanja. satanja/hex: pace-2022, June 2022. URL: https://doi.org/10.5281/zenodo.6609797.
  74. Robert Endre Tarjan. Depth-First Search and Linear Graph Algorithms. SIAM J. Comput., 1(2):146-160, 1972. URL: https://doi.org/10.1137/0201010.
  75. Szymon Wasik, Maciej Antczak, Jan Badura, Artur Laskowski, and Tomasz Sternal. Optil.io: Cloud based platform for solving optimization problems using crowdsourcing approach. In 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. Association for Computing Machinery. URL: https://doi.org/10.1145/2818052.2869098.
  76. Mingyu Xiao and Hiroshi Nagamochi. An improved exact algorithm for undirected feedback vertex set. J. Comb. Optim., 30(2):214-241, 2015. URL: https://doi.org/10.1007/s10878-014-9737-x.
  77. YuMingDu, QingYunZhang, and ShunGenZhang. pace-2022, June 2022. URL: https://doi.org/10.5281/zenodo.6644409.
  78. Zhang-qingyun. Zhang-qingyun/pace_2022_HUST_solver: pace_2022_HUST_solver, June 2022. URL: https://doi.org/10.5281/zenodo.6643002.
  79. Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propagation. Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002. URL: http://reports-archive.adm.cs.cmu.edu/anon/cald/CMU-CALD-02-107.pdf.
  80. Radovan Červený, Michal Dvořák, Xuan Thang Nguyen, Jan Pokorný, Lucie Procházková, Jaroslav Urban, Václav Blažej, Dušan Knop, Šimon Schierreich, and Ondřej Suchý. G2OAT solver for PACE 2022 (DFVS) exact track, June 2022. URL: https://doi.org/10.5281/zenodo.6637464.
  81. Radovan Červený, Michal Dvořák, Xuan Thang Nguyen, Jan Pokorný, Lucie Procházková, Jaroslav Urban, Václav Blažej, Dušan Knop, Šimon Schierreich, and Ondřej Suchý. G2OAT solver for PACE 2022 (DFVS) heuristic track, June 2022. URL: https://doi.org/10.5281/zenodo.6637495.
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