4 papers · 1 filter
On the Hardness of Strong Metric Dimension
Prafullkumar Tale
Let \(G\) be a connected simple undirected graph. A vertex \(w\) is said to \emph{strongly resolve} a pair of distinct vertices \(u, v \in V(G)\) if either there exists an isometri…
The Complexity of Contracting Bipartite Graphs into Small Cycles
R. Krithika, Roohani Sharma, Prafullkumar Tale
For a positive integer , the -Contractibility problem takes as input an undirected simple graph and determines whether can be transformed into a graph…
The Parameterized Complexity of Computing the VC-Dimension
Florent Foucaud, Harmender Gahlawat, Fionn Mc Inerney +1
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new re…
Problems in NP can Admit Double-Exponential Lower Bounds when Parameterized by Treewidth or Vertex Cover
Florent Foucaud, Esther Galby, Liana Khazaliya +4
Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and…