Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration

Authors Petr A. Golovach , Christian Komusiewicz , Dieter Kratsch, Van Bang Le

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Author Details

Petr A. Golovach
  • Department of Informatics, University of Bergen, Norway
Christian Komusiewicz
  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Germany
Dieter Kratsch
  • LGIMP, Université de Lorraine, Metz, France
Van Bang Le
  • Institut für Informatik, Universität Rostock, Germany


We dedicate this paper to the memory of our coauthor and friend Dieter Kratsch who recently passed away. Without Dieter, this paper would have never been written.

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Petr A. Golovach, Christian Komusiewicz, Dieter Kratsch, and Van Bang Le. Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Parameterized complexity and exact algorithms
  • enumeration problems
  • polynomial delay
  • output-sensitive algorithms
  • kernelization
  • structural parameterizations
  • matching cuts


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