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.
@InProceedings{curticapean:LIPIcs.IPEC.2018.1, author = {Curticapean, Radu}, title = {{Counting Problems in Parameterized Complexity}}, booktitle = {13th International Symposium on Parameterized and Exact Computation (IPEC 2018)}, pages = {1:1--1:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-084-2}, ISSN = {1868-8969}, year = {2019}, volume = {115}, editor = {Paul, Christophe and Pilipczuk, Michal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.1}, URN = {urn:nbn:de:0030-drops-102026}, doi = {10.4230/LIPIcs.IPEC.2018.1}, annote = {Keywords: counting complexity, parameterized complexity, graph motifs, perfect matchings, graph minor theory, Hamiltonian cycles} }
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