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The Fine-Grained Complexity of Pattern Counting Problems

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In this talk, I will present recent progress on the complexity of pattern counting problems from the perspectives of parameterized and fine-grained complexity theory. In the first part, I will introduce and discuss “Complexity Monotonicity”, a novel and powerful tool due to Curticapean, Dell and Marx (STOC 2017), which provides a unifying view on problems that require to count small structures in large networks. In the second part, I will give an overview over recent results on the complexity of induced subgraph counting , including, among others, a dichotomy theorem for counting small induced subgraphs that satisfy hereditary properties.

Based on joint works with Julian Dörfler, Jacob Focke, Johannes Schmitt, and Philip Wellnitz.

This talk is part of the Theoretical computer science seminar series.

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