A Polynomial Kernel for Funnel Arc Deletion Set

Author Marcelo Garlet Milani

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Marcelo Garlet Milani
  • Technische Universität Berlin, Chair of Logic and Semantics, Germany


We thank the referees for their numerous helpful comments.

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Marcelo Garlet Milani. A Polynomial Kernel for Funnel Arc Deletion Set. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In Directed Feedback Arc Set (DFAS) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider 𝒞-Arc Deletion Set (𝒞-ADS), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class 𝒞. In this work, we choose 𝒞 to be the class of funnels. Funnel-ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k. So far no polynomial kernel for this problem was known. Our main result is a kernel for Funnel-ADS with 𝒪(k⁶) many vertices and 𝒪(k⁷) many arcs, computable in 𝒪(nm) time, where n is the number of vertices and m the number of arcs of the input digraph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • graph editing
  • directed feedback arc set
  • parameterized algorithm
  • kernels
  • funnels


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  1. Faisal N Abu-Khzam. A kernelization algorithm for d-hitting set. Journal of Computer and System Sciences, 76(7):524-531, 2010. Google Scholar
  2. Akanksha Agrawal, Saket Saurabh, Roohani Sharma, and Meirav Zehavi. Kernels for deletion to classes of acyclic digraphs. Journal of Computer and System Sciences, 92:9-21, 2018. Google Scholar
  3. Jørgen Bang-Jensen, Alessandro Maddaloni, and Saket Saurabh. Algorithms and kernels for feedback set problems in generalizations of tournaments. Algorithmica, 76(2):320-343, 2016. Google Scholar
  4. Jianer Chen, Yang Liu, Songjian Lu, Barry O’sullivan, and Igor Razgon. A fixed-parameter algorithm for the directed feedback vertex set problem. Journal of the ACM (JACM), 55(5):21, 2008. Google Scholar
  5. Marek Cygan, Fedor V Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized algorithms, volume 4. Springer, 2015. Google Scholar
  6. Rodney G Downey and Michael R Fellows. Fundamentals of parameterized complexity, volume 4. Springer, 2013. Google Scholar
  7. Fedor V Fomin, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. Kernelization: theory of parameterized preprocessing. Cambridge University Press, 2019. Google Scholar
  8. Stefan Kratsch. Recent developments in kernelization: A survey. Bulletin of EATCS, 2(113), 2014. Google Scholar
  9. Daniel Lokshtanov, Neeldhara Misra, and Saket Saurabh. Kernelization-preprocessing with a guarantee. In The Multivariate Algorithmic Revolution and Beyond, pages 129-161. Springer, 2012. Google Scholar
  10. Daniel Lokshtanov, MS Ramanujan, Saket Saurabh, Roohani Sharma, and Meirav Zehavi. Wannabe bounded treewidth graphs admit a polynomial kernel for dfvs. In Workshop on Algorithms and Data Structures, pages 523-537. Springer, 2019. Google Scholar
  11. Marcelo Garlet Millani, Hendrik Molter, Rolf Niedermeier, and Manuel Sorge. Efficient algorithms for measuring the funnel-likeness of DAGs. In Jon Lee, Giovanni Rinaldi, and A. Ridha Mahjoub, editors, Combinatorial Optimization, pages 183-195, Cham, 2018. Springer International Publishing. Google Scholar
  12. Matthias Mnich and Erik Jan van Leeuwen. Polynomial kernels for deletion to classes of acyclic digraphs. Discrete Optimization, 25:48-76, 2017. Google Scholar