2015•Publications of the UdS (Saarland University)Open access

The simple, little and slow things count : on parameterized counting complexity

Radu Curticapean

Abstract

This contribution is intended to be a self-contained and minimally technical exposition of the material in my 2015 dissertation, which was supervised by Markus Blaser. As its title suggests, the thesis investigates the complexity of combinatorial counting problems in the frameworks of parameterized (and exponential-time) complexity. More precisely, the following specific settings are explored: Counting perfect matchings in structurally “simple” graphs, for instance, in graphs that exclude specific fixed minors Counting small subgraph patterns in large host graphs Exponential lower bounds on the running time needed to solve counting problems, assuming popular conjectures such as the exponentialtime hypothesis

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Key concepts: Parameterized complexity, Simple (philosophy), Counting problem, Mathematics, Exponential function, Computer science, Combinatorics, Exposition (narrative)