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

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

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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.

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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


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