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Counting Problems in Parameterized Complexity

Author Radu Curticapean

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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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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.

Cite As Get BibTex

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

Author Details

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

Funding

BARC is supported by Villum Foundation Grant No. 16582.

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