We introduce sharpSAT, a new #SAT solver that is based on the well known DPLL algorithm and techniques from SAT and #SAT solvers. Most importantly, we introduce an entirely new approach of coding… (More)

Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colorings or the number of independent… (More)

We study left-hand side restrictions of the induced subgraph isomorphism problem: Fixing a class C, for given graphs G ∈ C and arbitrary H we ask for induced subgraphs of H isomorphic to G. For the… (More)

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first… (More)

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition… (More)

Partition functions of certain classes of “spin glass” models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the… (More)

Kernelizations are an important tool in designing fixed parameter algorithms for parameterized decision problems. We introduce an analogous notion for counting problems, to wit, counting… (More)

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a… (More)

Homomorphisms between relational structures are not only fundamental mathematical objects, but are also of great importance in an applied computational context. Indeed, constraint satisfaction… (More)