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Many combinatorial problems involve determining whether a universe of $n$ elements contains a witness consisting of $k$ elements which have some specified property.
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Andreas Björklund, Petteri Kaski, and 𝖫 \mathsf{L} ukasz Kowalik, Fast witness extraction using a decision oracle , Algorithms (ESA 2014), LNCS, vol. 8737, Springer Berlin Heidelberg, 2014, pp. 149–160
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2010
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Andreas Björklund, Petteri Kaski, and 𝖫 \mathsf{L} ukasz Kowalik, Probably Optimal Graph Motifs , 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), LIPIcs, vol. 20, Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2013, pp. 20–31
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Nadia Creignou, Arne Meier, Julian-Steffen Müller, Johannes Schmidt, and Heribert Vollmer, Paradigms for parameterized enumeration , Mathematical Foundations of Computer Science (MFCS 2013), LNCS, vol. 8087, Springer Berlin Heidelberg, 2013, pp. 290–301
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Radu Curticapean, Counting matchings of size k is #W[1]-hard , Automata, Languages, and Programming (ICALP 2013), LNCS, vol. 7965, Springer Berlin Heidelberg, 2013, pp. 352–363
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Nadia Creignou, Raïda Ktari, Arne Meier, Julian-Steffen Müller, Frédéric Olive, and Heribert Vollmer, Parameterized enumeration for modification problems , Language and Automata Theory and Applications (LATA 2015), LNCS, vol. 8977, Springer International Publishing, 2015, pp. 524–536
2015
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Mark Jerrum and Kitty Meeks, The parameterised complexity of counting connected subgraphs and graph motifs , Journal of Computer and System Sciences 81
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Mark Jerrum and Kitty Meeks, Some hard families of parameterised counting problems , ACM Transactions on Computation Theory 7
2015
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Mark Jerrum and Kitty Meeks, The parameterised complexity of counting even and odd induced subgraphs , Combinatorica, 2016, doi:10.1007/s00493-016-3338-5
2016
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Kitty Meeks, The challenges of unbounded treewidth in parameterised subgraph counting problems , Discrete Applied Mathematics 198
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