The field of exact exponential time algorithms for non-deterministic polynomial-time hard
problems has thrived since the mid-2000s. While exhaustive search remains asymptotically …

The betweenness centrality of a vertex v is an important centrality measure that quantifies
how many optimal paths between pairs of other vertices visit v. Computing betweenness …

In this thesis, we study the parameterized complexity of counting problems, as introduced by
Flum and Grohe. This area mainly involves questions of the following kind: On inputs x with …

For a fixed graph property $\Phi $ and integer $ k\geq 1$, the problem $\#\mathrm
{IndSub}(\Phi, k) $ asks to count the induced $ k $-vertex subgraphs satisfying $\Phi $ in an …

We are motivated by a tantalizing open question in exact algorithms: can we detect whether
an $ n $-vertex directed graph $ G $ has a Hamiltonian cycle in time significantly less than …

We identify and study relevant structural parameters for the problem PerfMatch of counting
perfect matchings in a given input graph C. These generalize the well-known tractable …

We study the problem# INDSUB (Φ) of counting all induced subgraphs of size k in a graph G
that satisfy the property Φ. It is shown that, given any graph property Φ that distinguishes …

We study the problem $\#\mathrm {EdgeSub}(\Phi) $ of counting $ k $-edge subgraphs
satisfying a given graph property $\Phi $ in a large host graph $ G $. Building upon the …

We study the problem# IndSub (P) of counting all induced subgraphs of size k in a graph G
that satisfy the property P. This problem was introduced by Jerrum and Meeks and shown to …

Given a graph property $\Phi $, we consider the problem $\mathtt {EdgeSub}(\Phi) $, where
the input is a pair of a graph $ G $ and a positive integer $ k $, and the task is to decide …