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Sidestepping Barriers for Dominating Set in Parameterized Complexity

Authors Ioannis Koutis , Michał Włodarczyk , Meirav Zehavi

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Author Details

Ioannis Koutis
  • New Jersey Institute of Technology, NJ, USA
Michał Włodarczyk
  • University of Warsaw, Poland
Meirav Zehavi
  • Ben-Gurion University of the Negev, Beerhseba, Israel

Funding

Supported by BGU–NJIT Joint Seed Research Fund and ERC Starting Grant titled PARAPATH.

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Ioannis Koutis, Michał Włodarczyk, and Meirav Zehavi. Sidestepping Barriers for Dominating Set in Parameterized Complexity. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.IPEC.2023.31

Abstract

We study the classic Dominating Set problem with respect to several prominent parameters. Specifically, we present algorithmic results that sidestep time complexity barriers by the incorporation of either approximation or larger parameterization. Our results span several parameterization regimes, including: (i,ii,iii) time/ratio-tradeoff for the parameters treewidth, vertex modulator to constant treewidth and solution size; (iv,v) FPT-algorithms for the parameters vertex cover number and feedback edge set number; and (vi) compression for the parameter feedback edge set number.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Dominating Set
  • Parameterized Complexity
  • Approximation Algorithms

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References

  1. Saeed Akhoondian Amiri, Patrice Ossona de Mendez, Roman Rabinovich, and Sebastian Siebertz. Distributed domination on graph classes of bounded expansion. In Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, SPAA '18, pages 143-151, New York, NY, USA, 2018. Association for Computing Machinery. URL: https://doi.org/10.1145/3210377.3210383.
  2. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. URL: https://doi.org/10.1137/S0097539793251219.
  3. Hans L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci., 209(1-2):1-45, 1998. Google Scholar
  4. 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
  5. Marek Cygan, Lukasz Kowalik, and Mateusz Wykurz. Exponential-time approximation of weighted set cover. Inf. Process. Lett., 109(16):957-961, 2009. Google Scholar
  6. Marek Cygan, Geevarghese Philip, Marcin Pilipczuk, Michał Pilipczuk, and Jakub Onufry Wojtaszczyk. Dominating set is fixed parameter tractable in claw-free graphs. Theoretical Computer Science, 412(50):6982-7000, November 2011. URL: https://doi.org/10.1016/j.tcs.2011.09.010.
  7. Irit Dinur and David Steurer. Analytical approach to parallel repetition. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 624-633, 2014. Google Scholar
  8. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Springer Publishing Company, Incorporated, 2013. Google Scholar
  9. Friedrich Eisenbrand and Fabrizio Grandoni. On the complexity of fixed parameter clique and dominating set. Theoretical Computer Science, 326(1):57-67, 2004. URL: https://doi.org/10.1016/j.tcs.2004.05.009.
  10. Uriel Feige. A threshold of ln n for approximating set cover. J. ACM, 45(4):634-652, July 1998. URL: https://doi.org/10.1145/285055.285059.
  11. Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Dimitrios M. Thilikos. Linear kernels for (connected) dominating set on h-minor-free graphs. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '12, pages 82-93, USA, 2012. Society for Industrial and Applied Mathematics. Google Scholar
  12. Fedor V. Fomin and Dimitrios M. Thilikos. Dominating sets in planar graphs: Branch-width and exponential speed-up. SIAM Journal on Computing, 36(2):281-309, 2006. URL: https://doi.org/10.1137/S0097539702419649.
  13. Danny Hermelin, Matthias Mnich, Erik Jan van Leeuwen, and Gerhard J. Woeginger. Domination when the stars are out. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Zurich, Switzerland, July 4-8, 2011, Proceedings, Part I, pages 462-473, 2011. URL: https://doi.org/10.1007/978-3-642-22006-7_39.
  14. Tohru Kikuno, Noriyoshi Yoshida, and Yoshiaki Kakuda. A linear algorithm for the domination number of a series-parallel graph. Discret. Appl. Math., 5:299-311, 1983. Google Scholar
  15. Mikko Koivisto. An o*(2^n) algorithm for graph coloring and other partitioning problems via inclusion-exclusion. In 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), 21-24 October 2006, Berkeley, California, USA, Proceedings, pages 583-590, 2006. Google Scholar
  16. Daniel Lokshtanov, Dániel Marx, and Saket Saurabh. Known algorithms on graphs of bounded treewidth are probably optimal. ACM Trans. Algorithms, 14(2), April 2018. URL: https://doi.org/10.1145/3170442.
  17. Daniel Lokshtanov, Pranabendu Misra, M. S. Ramanujan, Saket Saurabh, and Meirav Zehavi. Fpt-approximation for FPT problems. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Virtual Conference, January 10 - 13, 2021, pages 199-218, 2021. URL: https://doi.org/10.1137/1.9781611976465.14.
  18. Dániel Marx. Parameterized Complexity of Independence and Domination on Geometric Graphs. In Hans L. Bodlaender and Michael A. Langston, editors, Parameterized and Exact Computation, pages 154-165, Berlin, Heidelberg, 2006. Springer Berlin Heidelberg. Google Scholar
  19. Mihai Pătraşcu and Ryan Williams. On the possibility of faster sat algorithms. In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '10, pages 1065-1075, USA, 2010. Society for Industrial and Applied Mathematics. Google Scholar
  20. Karthik C. S., Bundit Laekhanukit, and Pasin Manurangsi. On the parameterized complexity of approximating dominating set. J. ACM, 66(5), August 2019. URL: https://doi.org/10.1145/3325116.
  21. 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, pages 566-577, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg. Google Scholar
  22. Johan M.M. van Rooij and Hans L. Bodlaender. Exact algorithms for dominating set. Discrete Applied Mathematics, 159(17):2147-2164, 2011. URL: https://doi.org/10.1016/j.dam.2011.07.001.
  23. Vijay V. Vazirani. Approximation algorithms. Springer, 2001. URL: http://www.springer.com/computer/theoretical+computer+science/book/978-3-540-65367-7.
  24. Mingyu Xiao and Hiroshi Nagamochi. Exact algorithms for maximum independent set. Inf. Comput., 255:126-146, 2017. Google Scholar
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