Related papers: The Primal Pathwidth SETH
In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer…
We introduce a hierarchy of problems between the \textsc{Dominating Set} problem and the \textsc{Power Dominating Set} (PDS) problem called the $\ell$-round power dominating set ($\ell$-round PDS, for short) problem. For $\ell=1$, this is…
We study the parameterized complexity of approximating the $k$-Dominating Set (DomSet) problem where an integer $k$ and a graph $G$ on $n$ vertices are given as input, and the goal is to find a dominating set of size at most $F(k) \cdot k$…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…
Given a graph $G = (V,E)$, $A \subseteq V$, and integers $k$ and $\ell$, the \textsc{$(A,\ell)$-Path Packing} problem asks to find $k$ vertex-disjoint paths of length $\ell$ that have endpoints in $A$ and internal points in $V \setminus A$.…
De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted treewidth resulting…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such…
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing…
We investigate the complexity of parameterised holant problems p-$\mathrm{Holant}(\mathcal{S})$ for families of signatures $\mathcal{S}$. The parameterised holant framework was introduced by Curticapean in 2015 as a counter-part to the…
Deletion problems are those where given a graph $G$ and a graph property $\pi$, the goal is to find a subset of edges such that after its removal the graph $G$ will satisfy the property $\pi$. Typically, we want to minimize the number of…
In this paper, we introduce a general framework for fine-grained reductions of approximate counting problems to their decision versions. (Thus we use an oracle that decides whether any witness exists to multiplicatively approximate the…
Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…
Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems…