Related papers: Meta-Kernelization using Well-Structured Modulator…
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…
Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…
Makespan minimization (on parallel identical or unrelated machines) is arguably the most natural and studied scheduling problem. A common approach in practical algorithm design is to reduce the size of a given instance by a fast…
Dealing with NP-hard problems, kernelization is a fundamental notion for polynomial-time data reduction with performance guarantees: in polynomial time, a problem instance is reduced to an equivalent instance with size upper-bounded by a…
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…
The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic…
An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…
In convolutional neural network-based character recognition, pooling layers play an important role in dimensionality reduction and deformation compensation. However, their kernel shapes and pooling operations are empirically predetermined;…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous…
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…
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…
We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…
Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…
Enumeration kernelization for parameterized enumeration problems was defined by Creignou et al. [Theory Comput. Syst. 2017] and was later refined by Golovach et al. [J. Comput. Syst. Sci. 2022, STACS 2021] to polynomial-delay enumeration…
The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…
The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…
Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model…
Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…