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Counting Problems in Parameterized Complexity

Author Radu Curticapean



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Radu Curticapean
  • Basic Algorithms Research Copenhagen (BARC) and IT University of Copenhagen, Copenhagen, Denmark

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Radu Curticapean. Counting Problems in Parameterized Complexity. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 1:1-1:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.IPEC.2018.1

Abstract

This survey is an invitation to parameterized counting problems for readers with a background in parameterized algorithms and complexity. After an introduction to the peculiarities of counting complexity, we survey the parameterized approach to counting problems, with a focus on two topics of recent interest: Counting small patterns in large graphs, and counting perfect matchings and Hamiltonian cycles in well-structured graphs. While this survey presupposes familiarity with parameterized algorithms and complexity, we aim at explaining all relevant notions from counting complexity in a self-contained way.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Problems, reductions and completeness
Keywords
  • counting complexity
  • parameterized complexity
  • graph motifs
  • perfect matchings
  • graph minor theory
  • Hamiltonian cycles

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