Related papers: Kernelization Lower Bounds for Finding Constant-Si…
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…
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
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 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…
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 parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
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…
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…
This paper focuses on kernelization algorithms for the fundamental Knapsack problem. A kernelization algorithm (or kernel) is a polynomial-time reduction from a problem onto itself, where the output size is bounded by a function of some…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
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…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
The task of listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to…
An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a…
Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…
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…