A 9/4-Approximation for Directed Feedback Vertex Sets in Quasi-Transitive Digraphs

A $2$-Approximation for Directed Feedback Vertex Set in Locally Semicomplete and Quasi-Transitive Digraphs

A \emph{directed feedback vertex set} of a digraph is a set of vertices whose removal destroys all directed cycles. The \textsc{Directed Feedback Vertex Set} (\textsc{DFVS}) problem asks for such a set of minimum cardinality or minimum total weight. Although general \textsc{DFVS} admits no constant-factor approximation...

A BRANCH AND BOUND ALGORITHM FOR FINDING THE POSITIVE INFLUENCE DOMINATING SET ON CHORDAL GRAPHS

This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.

A Polynomial Kernel for Planar Directed Feedback Vertex Set

The Directed Feedback Vertex Set problem (DFVS) asks whether a digraph can be made acyclic by deleting at most $k$ vertices. Whether DFVS admits a polynomial kernel parameterized by $k$ is a major open problem in kernelization, even for planar digraphs. We resolve the planar case by giving a deterministic kernel with $...

Exponential Lower Bounds for Integer-Weighted Shortest-Paths Preservers of DAGs

We study a graph simplification problem introduced by Bernstein, Bodwin, and Wein [ITCS'24]. We start with a graph with arbitrarily large positive edge weights and the goal is to reweight the edges to small aspect ratio (ratio between largest and smallest weight) while preserving the shortest paths structure (the seque...

Perfect Italian Domination on Structured Bipartite Graphs: Algorithms, Parameterization, and Hardness

A perfect Italian dominating function assigns values in {0,1,2} to the vertices of a graph so that every zero-valued vertex has a neighbor-value sum of exactly two. We determine the computational complexity of the problem for bipartite graphs whose neighborhoods are subtrees of a simple host tree. On convex bipartite g...

Upper Clique Transversal on Interval Graphs and Beyond