5 papers
Algorithms and data structures for first-order logic with connectivity under vertex failures
Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz +2
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer k, we can in…
First-Order Logic with Connectivity Operators
Nicole Schirrmacher, Sebastian Siebertz, Alexandre Vigny
First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem, parameterized by solution size. On the other hand, F…
Recursive Backdoors for SAT
Nikolas Mählmann, Sebastian Siebertz, Alexandre Vigny
A strong backdoor in a formula of propositional logic to a tractable class of formulas is a set of variables of such that every assignment of the variable…
Constant round distributed domination on graph classes with bounded expansion
Simeon Kublenz, Sebastian Siebertz, Alexandre Vigny
We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with boun…
Dynamic Query Evaluation Over Structures with Low Degree
Alexandre Vigny
We consider the evaluation of first-order queries over classes of databases that have bounded degree and low degree. More precisely, given a query and a database, we want to effici…