Parameterized and Counting Algorithms and Complexity

Parameterized complexity analyzes how different parameters of the input influence the complexity of hard algorithmic problems. The general goal is to show with fixed-parameter tractability results that the combinatorial explosion can be confined to certain well-defined parameters, or to understand why such algorithms are not possible. An interesting class of hard problems that we consider are counting problems (where the goal is to count all solutions), as they may allow for interesting phenomena that are not observed in the corresponding decision problems.