Related papers: PACE Solver Description: A Heuristic Directed Feed…
A {\em tournament} is a directed graph $T$ such that every pair of vertices is connected by an arc. A {\em feedback vertex set} is a set $S$ of vertices in $T$ such that $T - S$ is acyclic. We consider the {\sc Feedback Vertex Set} problem…
The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph~$G$ and seeks a smallest vertex set~$S$ that hits all cycles in $G$. This is one of Karp's 21 $\mathsf{NP}$-complete problems. Resolving the parameterized…
The 2024 PACE Challenge focused on the One-Sided Crossing Minimization (OCM) problem, which aims to minimize edge crossings in a bipartite graph with a fixed order in one partition and a free order in the other. We describe our OCM solver…
A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph. The feedback vertex set problem consists of constructing a FVS of size less than a certain given value.…
Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower…
We study the parameterized complexity of a robust generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem; we are given a graph G with edges labeled with group elements, and the goal is to…
In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…
The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $\nu \subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus \nu$…
We propose a new approach to the Directed Feedback Vertex Set Problem (DFVSP), where the input is a directed graph and the solution is a minimum set of vertices whose removal makes the graph acyclic. Our approach, implemented in the solver…
Let G=(A,B,E) be a bipartite graph with color classes A and B. The graph G is chordal bipartite if G has no induced cycle of length more than four. Let G=(V,E) be a graph. A feedback vertex set F is a set of vertices F subset V such that…
This work investigates the parameterized complexity of three related graph modification problems. Given a directed graph, a distinguished vertex, and a positive integer k, Minimum Indegree Deletion asks for a vertex subset of size at most k…
We present two algorithms for the minimum feedback vertex set problem in planar graphs: an $O(n \log n)$ PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local search. We implemented these…
Directed networks such as gene regulation networks and neural networks are connected by arcs (directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which lead to complex…
In this note we study the computational complexity of feedback arc set counting problems in directed graphs, highlighting some subtle yet common properties of counting classes. Counting the number of feedback arc sets of cardinality $k$ and…
Given a directed graph, the Minimum Feedback Arc Set (FAS) problem asks for a minimum (size) set of arcs in a directed graph, which, when removed, results in an acyclic graph. In a seminal paper, Berger and Shor [1], in 1990, developed…
In this paper we study a maximization version of the classical Feedback Vertex Set (FVS) problem, namely, the Max Min FVS problem, in the realm of parameterized complexity. In this problem, given an undirected graph $G$, a positive integer…
In directed graphs, we investigate the problems of finding: 1) a minimum feedback vertex set (also called the Feedback Vertex Set problem, or MFVS), 2) a feedback vertex set inducing an acyclic graph (also called the Vertex 2-Coloring…
A {\em bipartite tournament} is a directed graph $T:=(A \cup B, E)$ such that every pair of vertices $(a,b), a\in A,b\in B$ are connected by an arc, and no arc connects two vertices of $A$ or two vertices of $B$. A {\em feedback vertex set}…
We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related…
Getting a labeling of vertices close to the structure of the graph has been proved to be of interest in many applications e.g., to follow smooth signals indexed by the vertices of the network. This question can be related to a graph…