Related papers: A Polynomial Kernel for Funnel Arc Deletion Set

Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…

Deep learning algorithms, in particular 2D and 3D fully convolutional neural networks (FCNs), have rapidly become the mainstream methodology for volumetric medical image segmentation. However, 2D convolutions cannot fully leverage the rich…

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…

Accurate segmentation of organs-at-risks (OARs) is a precursor for optimizing radiation therapy planning. Existing deep learning-based multi-scale fusion architectures have demonstrated a tremendous capacity for 2D medical image…

It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…

3D Convolution Neural Networks (CNNs) have been widely applied to 3D scene understanding, such as video analysis and volumetric image recognition. However, 3D networks can easily lead to over-parameterization which incurs expensive…

The diameter of a directed graph is the maximum distance between any pair of vertices. We study a problem that generalizes \textsc{Oriented Diameter}: For a given directed graph and a positive integer $d$, what is the minimum number of arc…

The searching procedure of neural architecture search (NAS) is notoriously time consuming and cost prohibitive.To make the search space continuous, most existing gradient-based NAS methods relax the categorical choice of a particular…

An orientation $D$ of a graph $G=(V,E)$ is a digraph obtained from $G$ by replacing each edge by exactly one of the two possible arcs with the same end vertices. For each $v \in V(G)$, the indegree of $v$ in $D$, denoted by $d^-_D(v)$, is…

A knot $K$ in a directed graph $D$ is a strongly connected component of size at least two such that there is no arc $(u,v)$ with $u \in V(K)$ and $v\notin V(K)$. Given a directed graph $D=(V,E)$, we study Knot-Free Vertex Deletion (KFVD),…

Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…

Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore,…

This paper describes the transformation of a traditional in-silico classification network into an optical fully convolutional neural network with high-resolution feature maps and kernels. When using the free-space 4f system to accelerate…

We study the parameterized and classical complexity of two related problems on undirected graphs $G=(V,E)$. In Strong Triadic Closure we aim to label the edges in $E$ as strong and weak such that at most~$k$ edges are weak and $G$ contains…

In the Planar Disjoint Paths problem, one is given an undirected planar graph with a set of $k$ vertex pairs $(s_i,t_i)$ and the task is to find $k$ pairwise vertex-disjoint paths such that the $i$-th path connects $s_i$ to $t_i$. We study…

We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems:…

We define and study a new structural parameter for directed graphs, which we call \emph{ear anonymity}. Our parameter aims to generalize the useful properties of \emph{funnels} to larger digraph classes. In particular, funnels are exactly…

Convolutional neural network (CNN) slides a kernel over the whole image to produce an output map. This kernel scheme reduces the number of parameters with respect to a fully connected neural network (NN). While CNN has proven to be an…

A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general…

The Flow Decomposition problem, which asks for the smallest set of weighted paths that "covers" a flow on a DAG, has recently been used as an important computational step in transcript assembly. We prove the problem is in FPT when…