There and Back Again: On Applying Data Reduction Rules by Undoing Others

Authors Aleksander Figiel, Vincent Froese, André Nichterlein , Rolf Niedermeier

Thumbnail PDF


  • Filesize: 1.13 MB
  • 15 pages

Document Identifiers

Author Details

Aleksander Figiel
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Vincent Froese
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
André Nichterlein
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany


This work is based on the first author’s master’s thesis. In memory of Rolf Niedermeier, our colleague, friend, and mentor, who sadly passed away before this paper was published.

Cite AsGet BibTex

Aleksander Figiel, Vincent Froese, André Nichterlein, and Rolf Niedermeier. There and Back Again: On Applying Data Reduction Rules by Undoing Others. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Data reduction rules are an established method in the algorithmic toolbox for tackling computationally challenging problems. A data reduction rule is a polynomial-time algorithm that, given a problem instance as input, outputs an equivalent, typically smaller instance of the same problem. The application of data reduction rules during the preprocessing of problem instances allows in many cases to considerably shrink their size, or even solve them directly. Commonly, these data reduction rules are applied exhaustively and in some fixed order to obtain irreducible instances. It was often observed that by changing the order of the rules, different irreducible instances can be obtained. We propose to "undo" data reduction rules on irreducible instances, by which they become larger, and then subsequently apply data reduction rules again to shrink them. We show that this somewhat counter-intuitive approach can lead to significantly smaller irreducible instances. The process of undoing data reduction rules is not limited to "rolling back" data reduction rules applied to the instance during preprocessing. Instead, we formulate so-called backward rules, which essentially undo a data reduction rule, but without using any information about which data reduction rules were applied to it previously. In particular, based on the example of Vertex Cover we propose two methods applying backward rules to shrink the instances further. In our experiments we show that this way smaller irreducible instances consisting of real-world graphs from the SNAP and DIMACS datasets can be computed.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Branch-and-bound
  • Kernelization
  • Preprocessing
  • Vertex Cover


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


  1. Faisal N. Abu-Khzam, Rebecca L. Collins, Michael R. Fellows, Michael A. Langston, W. Henry Suters, and Christopher T. Symons. Kernelization algorithms for the vertex cover problem: Theory and experiments. In Proceedings of the 6th Workshop on Algorithm Engineering and Experiments and the 1st Workshop on Analytic Algorithmics and Combinatorics, pages 62-69. SIAM, 2004. Google Scholar
  2. Faisal N. Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, and Darren Strash. Recent advances in practical data reduction. CoRR, abs/2012.12594, 2020. URL:
  3. Takuya Akiba and Yoichi Iwata. Branch-and-reduce exponential/fpt algorithms in practice: A case study of vertex cover. Theoretical Computer Science, 609:211-225, 2016. URL:
  4. Gabriela Alexe, Peter L. Hammer, Vadim V. Lozin, and Dominique de Werra. Struction revisited. Discrete Applied Mathematics, 132(1-3):27-46, 2003. URL:
  5. David A. Bader, Henning Meyerhenke, Peter Sanders, and Dorothea Wagner, editors. Graph Partitioning and Graph Clustering, 10th DIMACS Implementation Challenge Workshop, volume 588 of Contemporary Mathematics. American Mathematical Society, 2013. URL:
  6. M. Ayaz Dzulfikar, Johannes K. Fichte, and Markus Hecher. Pace2019: Track 1 - vertex cover instances, July 2019. URL:
  7. M. Ayaz Dzulfikar, Johannes Klaus Fichte, and Markus Hecher. The PACE 2019 parameterized algorithms and computational experiments challenge: The fourth iteration (invited paper). In Proccedings of the 14th International Symposium on Parameterized and Exact Computation (IPEC 2019), volume 148 of LIPIcs, pages 25:1-25:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL:
  8. Hartmut Ehrig, Claudia Ermel, Falk Hüffner, Rolf Niedermeier, and Olga Runge. Confluence in data reduction: Bridging graph transformation and kernelization. Computability, 2(1):31-49, 2013. URL:
  9. 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 - Essays Dedicated to Juraj Hromkovič on the Occasion of His 60th Birthday, volume 11011 of LNCS, pages 330-356. Springer, 2018. URL:
  10. Aleksander Figiel, Vincent Froese, André Nichterlein, and Rolf Niedermeier. There and back again: On applying data reduction rules by undoing others, 2022. URL:
  11. Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. Kernelization: Theory of Parameterized Preprocessing. Cambridge University Press, 2019. URL:
  12. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979. Google Scholar
  13. Alexander Gellner, Sebastian Lamm, Christian Schulz, Darren Strash, and Bogdán Zaválnij. Boosting data reduction for the maximum weight independent set problem using increasing transformations. In Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX 2021), pages 128-142. SIAM, 2021. URL:
  14. Demian Hespe, Sebastian Lamm, Christian Schulz, and Darren Strash. WeGotYouCovered: The Winning Solver from the PACE 2019 Challenge, Vertex Cover Track. In Proceedings of the SIAM Workshop on Combinatorial Scientific Computing, CSC 2020, pages 1-11. SIAM, 2020. URL:
  15. Richard M. Karp. Reducibility among Combinatorial Problems, pages 85-103. Springer US, 1972. URL:
  16. Tomohiro Koana, Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche. Data reduction for maximum matching on real-world graphs: Theory and experiments. ACM Journal of Experimental Algorithmics, 26, 2021. URL:
  17. Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford large network dataset collection., June 2014.
  18. Karsten Weihe. Covering trains by stations or the power of data reduction. In Proceedings 1st Conference on Algorithms and Experiments (ALEX98), pages 1-8, February 1998. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail