Related papers: Lossy Kernelization
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) with at least $k$ leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized…
It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas -- including not only…
The Identifying Code (IC) problem seeks a vertex subset whose intersection with every vertex's closed neighborhood is unique, enabling fault detection in multiprocessor systems and practical uses in identity verification, environmental…
We examine a parameterized complexity class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on a proposal by Kwisthout in [15,16]. We prove…
Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
The input to the NP-hard Point Line Cover problem (PLC) consists of a set $P$ of $n$ points on the plane and a positive integer $k$, and the question is whether there exists a set of at most $k$ lines which pass through all points in $P$. A…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graph G has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial…
Meta-theorems for polynomial (linear) kernels have been the subject of intensive research in parameterized complexity. Heretofore, meta-theorems for linear kernels exist on graphs of bounded genus, $H$-minor-free graphs, and…
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…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…
We propose a preprocessing algorithm for the multiway cut problem that establishes its polynomial kernelizability when the difference between the parameter $k$ and the size of the smallest isolating cut is at most $log(k)$. To the best of…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…