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Dynamic Parameterized Feedback Problems in Tournaments

Authors Anna Zych-Pawlewicz , Marek Żochowski

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LIPIcs.IPEC.2024.22.pdf
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Author Details

Anna Zych-Pawlewicz
  • Institute of Informatics, University of Warsaw, Poland
Marek Żochowski
  • Institute of Informatics, University of Warsaw, Poland

Funding

National Science Centre, Poland, Grant 2017/26/D/ST6/00264

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Anna Zych-Pawlewicz and Marek Żochowski. Dynamic Parameterized Feedback Problems in Tournaments. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.22

Abstract

In this paper we present the first dynamic algorithms for the problem of K-Feedback Arc Set in Tournaments (K-Fast) and the problem of K-Feedback Vertex Set in Tournaments (K-Fvst). Our algorithms maintain a dynamic tournament on n vertices altered by redirecting the arcs, and answer if the tournament admits a feedback arc set (or respectively feedback vertex set) of size at most K, for some chosen parameter K. For dynamic K-Fast we offer two algorithms. In the promise model, where we are guaranteed, that the size of the solution does not exceed g(K) for some computable function g, we give an O(√g(K)) update and O(3^K K √K) query algorithm. In the general setting without any promise, we offer an O(log² n) update and O(3^K K log² n) query time algorithm for dynamic K-Fast. For dynamic K-Fvst we offer an algorithm working in the promise model, which admits O(g⁵(K)) update and O(3^K K³ g(K)) query time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Data structures design and analysis
Keywords
  • dynamic algorithms
  • parameterized algorithms
  • feedback arc set
  • feedback vertex set
  • tournaments

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References

  1. Josh Alman, Matthias Mnich, and Virginia Vassilevska Williams. Dynamic parameterized problems and algorithms. ACM Trans. Algorithms, 16(4), July 2020. URL: https://doi.org/10.1145/3395037.
  2. Noga Alon. Ranking tournaments. SIAM Journal on Discrete Mathematics, 20(1):137-142, 2006. URL: https://doi.org/10.1137/050623905.
  3. Noga Alon, Daniel Lokshtanov, and Saket Saurabh. Fast FAST. In Susanne Albers, Alberto Marchetti-Spaccamela, Yossi Matias, Sotiris E. Nikoletseas, and Wolfgang Thomas, editors, Automata, Languages and Programming, 36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part I, volume 5555 of Lecture Notes in Computer Science, pages 49-58. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-02927-1_6.
  4. Jeffrey Banks. Sophisticated voting outcomes and agenda control. Working Papers 524, California Institute of Technology, Division of the Humanities and Social Sciences, 1984. URL: https://EconPapers.repec.org/RePEc:clt:sswopa:524.
  5. Jiehua Chen, Wojciech Czerwiński, Yann Disser, Andreas Emil Feldmann, Danny Hermelin, Wojciech Nadara, Marcin Pilipczuk, Michał Pilipczuk, Manuel Sorge, Bartłomiej Wróblewski, and Anna Zych-Pawlewicz. Efficient fully dynamic elimination forests with applications to detecting long paths and cycles. In Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '21, pages 796-809, USA, 2021. Society for Industrial and Applied Mathematics. URL: https://doi.org/10.1137/1.9781611976465.50.
  6. Don Coppersmith, Lisa K. Fleischer, and Atri Rurda. Ordering by weighted number of wins gives a good ranking for weighted tournaments. ACM Trans. Algorithms, 6(3), July 2010. URL: https://doi.org/10.1145/1798596.1798608.
  7. Zdenek Dvořák, Martin Kupec, and Vojtech Tůma. A dynamic data structure for MSO properties in graphs with bounded tree-depth. In 22th Annual European Symposium on Algorithms, ESA 2014, volume 8737 of Lecture Notes in Computer Science, pages 334-345. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-44777-2_28.
  8. Zdenek Dvořák and Vojtech Tůma. A dynamic data structure for counting subgraphs in sparse graphs. In 13th International Symposium on Algorithms and Data Structures, WADS 2013, volume 8037 of Lecture Notes in Computer Science, pages 304-315. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-40104-6_27.
  9. Pál Erdös and John W. Moon. On sets of consistent arcs in a tournament. Canadian Mathematical Bulletin, 8:269-271, 1965. URL: https://api.semanticscholar.org/CorpusID:19010097.
  10. Uriel Feige. Faster fast(feedback arc set in tournaments), 2009. URL: https://arxiv.org/abs/0911.5094.
  11. W Fernandez de la Vega. On the maximum cardinality of a consistent set of arcs in a random tournament. Journal of Combinatorial Theory, Series B, 35(3):328-332, 1983. URL: https://doi.org/10.1016/0095-8956(83)90060-6.
  12. Fedor V. Fomin and Michał Pilipczuk. On width measures and topological problems on semi-complete digraphs. Journal of Combinatorial Theory, Series B, 138:78-165, 2019. URL: https://doi.org/10.1016/j.jctb.2019.01.006.
  13. Serge Gaspers and Matthias Mnich. Feedback vertex sets in tournaments. In Mark de Berg and Ulrich Meyer, editors, Algorithms - ESA 2010, pages 267-277, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-15775-2_23.
  14. Jacob Holm, Kristian de Lichtenberg, and Mikkel Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM, 48(4):723-760, July 2001. URL: https://doi.org/10.1145/502090.502095.
  15. Yoichi Iwata and Keigo Oka. Fast dynamic graph algorithms for parameterized problems. In 14th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2014, volume 8503 of Lecture Notes in Computer Science, pages 241-252. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-08404-6_21.
  16. Claire Kenyon-Mathieu and Warren Schudy. How to rank with few errors. In Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, STOC '07, pages 95-103, New York, NY, USA, 2007. Association for Computing Machinery. URL: https://doi.org/10.1145/1250790.1250806.
  17. Tuukka Korhonen, Konrad Majewski, Wojciech Nadara, Michał Pilipczuk, and Marek Sokołowski. Dynamic treewidth, 2023. URL: https://arxiv.org/abs/2304.01744.
  18. R. Krithika, Abhishek Sahu, Saket Saurabh, and Meirav Zehavi. The parameterized complexity of packing arc-disjoint cycles in tournaments, 2018. URL: https://arxiv.org/abs/1802.07090.
  19. Mithilesh Kumar and Daniel Lokshtanov. Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments. In Nicolas Ollinger and Heribert Vollmer, editors, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016), volume 47 of Leibniz International Proceedings in Informatics (LIPIcs), pages 49:1-49:13, Dagstuhl, Germany, 2016. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.STACS.2016.49.
  20. 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.
  21. Konrad Majewski, Michał Pilipczuk, and Marek Sokołowski. Maintaining CMSO2 Properties on Dynamic Structures with Bounded Feedback Vertex Number. In Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté, editors, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023), volume 254 of Leibniz International Proceedings in Informatics (LIPIcs), pages 46:1-46:13, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.STACS.2023.46.
  22. Matthias Mnich, Virginia Vassilevska Williams, and László A. Végh. A 7/3-Approximation for Feedback Vertex Sets in Tournaments. In Piotr Sankowski and Christos Zaroliagis, editors, 24th Annual European Symposium on Algorithms (ESA 2016), volume 57 of Leibniz International Proceedings in Informatics (LIPIcs), pages 67:1-67:14, Dagstuhl, Germany, 2016. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ESA.2016.67.
  23. Jędrzej Olkowski, Michał Pilipczuk, Mateusz Rychlicki, Karol Węgrzycki, and Anna Zych-Pawlewicz. Dynamic Data Structures for Parameterized String Problems. In Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté, editors, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023), volume 254 of Leibniz International Proceedings in Informatics (LIPIcs), pages 50:1-50:22, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.STACS.2023.50.
  24. Venkatesh Raman and Saket Saurabh. Parameterized algorithms for feedback set problems and their duals in tournaments. Theoretical Computer Science, 351(3):446-458, 2006. Parameterized and Exact Computation. URL: https://doi.org/10.1016/j.tcs.2005.10.010.
  25. K.B. Reid and E.T. Parker. Disproof of a conjecture of erdös and moser on tournaments. Journal of Combinatorial Theory, 9(3):225-238, 1970. URL: https://doi.org/10.1016/S0021-9800(70)80061-8.
  26. E. Speckenmeyer. On feedback problems in digraphs. In Proceedings of the Fifteenth International Workshop on Graph-Theoretic Concepts in Computer Science, WG '89, pages 218-231, Berlin, Heidelberg, 1990. Springer-Verlag. Google Scholar
  27. Anke van Zuylen, Rajneesh Hegde, Kamal Jain, and David P. Williamson. Deterministic pivoting algorithms for constrained ranking and clustering problems. In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '07, pages 405-414, USA, 2007. Society for Industrial and Applied Mathematics. URL: http://dl.acm.org/citation.cfm?id=1283383.1283426.
  28. Anna Zych-Pawlewicz and Marek Żochowski. Dynamic parameterized feedback problems in tournaments, 2024. URL: https://doi.org/10.48550/arXiv.2404.12907.
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