相关论文: A Polynomial Kernel for Funnel Arc Deletion Set

In the Max $k$-Weight SAT (aka Max SAT with Cardinality Constraint) problem, we are given a CNF formula with $n$ variables and $m$ clauses together with a positive integer $k$. The goal is to find an assignment where at most $k$ variables…

In the Trivially Perfect Editing problem one is given an undirected graph $G = (V,E)$ and an integer $k$ and seeks to add or delete at most $k$ edges in $G$ to obtain a trivially perfect graph. In a recent work, Dumas, Perez and Todinca…

Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…

A graph is $c$-closed when every pair of nonadjacent vertices has at most $c-1$ common neighbors. In $c$-Closed Vertex Deletion, the input is a graph $G$ and an integer $k$ and we ask whether $G$ can be transformed into a $c$-closed graph…

For a graph class $\mathcal{C}$, the $\mathcal{C}$-Edge-Deletion problem asks for a given graph $G$ to delete the minimum number of edges from $G$ in order to obtain a graph in $\mathcal{C}$. We study the $\mathcal{C}$-Edge-Deletion problem…

A subgraph $T$ of a digraph $D$ is an {\em out-branching} if $T$ is an oriented spanning tree with only one vertex of in-degree zero (called the {\em root}). The vertices of $T$ of out-degree zero are {\em leaves}. In the {\sc Directed…

In this paper, we pursue the investigations started in \cite{Mas-You} where the authors provide a construction of the Dunkl intertwining operator for a large subset of the set of regular multiplicity values. More precisely, we make concrete…

The three-in-a-tree problem asks for an induced tree of the input graph containing three mandatory vertices. In 2006, Chudnovsky and Seymour [Combinatorica, 2010] presented the first polynomial time algorithm for this problem, which has…

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example,…

In recent years, two competitive time series classification models, namely, ROCKET and MINIROCKET, have garnered considerable attention due to their low training cost and high accuracy. However, they rely on a large number of random 1-D…

A typical example that behaves computationally different in subclasses of chordal graphs is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a vertex-weighted graph $G=(V,E)$ and a set $S\subseteq V$, the \textsc{Subset…

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 $G\setminus \varepsilon$, $G\setminus \nu$…

Automated segmentation of individual calf muscle compartments from 3D magnetic resonance (MR) images is essential for developing quantitative biomarkers for muscular disease progression and its prediction. Achieving clinically acceptable…

We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an…

For $\alpha\colon\mathbb{N}\rightarrow\mathbb{R}$, an $\alpha$-approximate bi-kernel is a polynomial-time algorithm that takes as input an instance $(I, k)$ of a problem $Q$ and outputs an instance $(I',k')$ of a problem $Q'$ of size…

It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…

In the problem {\sc Min-DESC}, we are given a digraph $D$ and an integer $k$, and asked if there exists a set $A'$ of at most $k$ arcs in $D$, such that if we remove the arcs of $A'$, in the resulting digraph every strong component is…

The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive…

The $d$-Hitting Set problem is a fundamental problem in parameterized complexity, which asks whether a given hypergraph contains a vertex subset $S$ of size at most $k$ that intersects every hyperedge (i.e., $S \cap e \neq \emptyset$ for…

We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a…