Related papers: Computing Hitting Set Kernels By AC^0-Circuits
In 1985, Chv\'{a}tal introduced the concept of star cutsets as a means to investigate the properties of perfect graphs, which inspired many researchers to study cutsets with some specific structures, for example, star cutsets, clique…
A range family $\mathcal{R}$ is a family of subsets of $\mathbb{R}^d$, like all halfplanes, or all unit disks. Given a range family $\mathcal{R}$, we consider the $m$-uniform range capturing hypergraphs $\mathcal{H}(V,\mathcal{R},m)$ whose…
It is well known that determining if a digraph has a kernel is an NP-complete problem. However, Topp proved that when subdividing every arc of a digraph we obtain a digraph with a kernel. In this paper we define the kernel subdivision…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…
Given an ordering of the vertices of a graph, the cost of covering an edge is the smaller number of its two ends. The minimum sum vertex cover problem asks for an ordering that minimizes the total cost of covering all edges. We consider…
A subset $M$ of the edges of a graph or hypergraph is hitting if $M$ covers each vertex of $H$ at least once, and $M$ is $t$-shallow if it covers each vertex of $H$ at most $t$ times. We consider the existence of shallow hitting edge sets…
We study the problem of counting $k$-hypergraphlets, an interesting but surprisingly ignored primitive, with the aim of understanding whether efficient algorithms exist. To this end, we consider color coding, a well-known technique for…
An induced subgraph is called an induced matching if each vertex is a degree-1 vertex in the subgraph. The \textsc{Almost Induced Matching} problem asks whether we can delete at most $k$ vertices from the input graph such that the remaining…
In a (parameterized) graph edge modification problem, we are given a graph $G$, an integer $k$ and a (usually well-structured) class of graphs $\mathcal{G}$, and ask whether it is possible to transform $G$ into a graph $G' \in \mathcal{G}$…
Subgraph counting aims to count the number of occurrences of a subgraph T (aka as a template) in a given graph G. The basic problem has found applications in diverse domains. The problem is known to be computationally challenging - the…
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
A kernelization for a parameterized decision problem $\mathcal{Q}$ is a polynomial-time preprocessing algorithm that reduces any parameterized instance $(x,k)$ into an instance $(x',k')$ whose size is bounded by a function of $k$ alone and…
The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive…
We consider a natural generalization of Vertex Cover: the Subset Vertex Cover problem, which is to decide for a graph $G=(V,E)$, a subset $T\subseteq V$ and integer $k$, if $V$ has a subset $S$ of size at most $k$, such that $S$ contains at…
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
Tracking of moving objects is crucial to security systems and networks. Given a graph $G$, terminal vertices $s$ and $t$, and an integer $k$, the \textsc{Tracking Paths} problem asks whether there exists at most $k$ vertices, which if…
In this paper, we devise a scheme for kernelizing, in sublinear space and polynomial time, various problems on planar graphs. The scheme exploits planarity to ensure that the resulting algorithms run in polynomial time and use O((sqrt(n) +…
We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…