Related papers: Subexponential parameterized algorithms and kernel…
We study the \textsc{$\alpha$-Fixed Cardinality Graph Partitioning ($\alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two…
Given a graph $G$ and an integer $k$, the $H$-free Edge Deletion problem asks whether there exists a set of at most $k$ edges of $G$ whose deletion makes $G$ free of induced copies of $H$. Significant attention has been given to the…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least…
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
In this paper we investigate the existence of subexponential parameterized algorithms of three fundamental cycle-hitting problems in geometric graph classes. The considered problems, \textsc{Triangle Hitting} (TH), \textsc{Feedback Vertex…
We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an…
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 monitoring edge-geodetic set of a graph is a subset $M$ of its vertices such that for every edge $e$ in the graph, deleting $e$ increases the distance between at least one pair of vertices in $M$. We study the following computational…
The family of $(k, \ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic challenge is to compute a…
We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced…
A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as…
It has long been known that Feedback Vertex Set can be solved in time $2^{\mathcal{O}(w\log w)}n^{\mathcal{O}(1)}$ on $n$-vertex graphs of treewidth $w$, but it was only recently that this running time was improved to…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
The $H$-Free Edge Deletion problem asks, for a given graph $G$ and an integer $k$, whether it is possible to delete at most $k$ edges from $G$ to make it $H$-free, that is, not containing $H$ as an induced subgraph. The $H$-Free Edge…