Related papers: A Hierarchy of Polynomial Kernels
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…
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…
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…
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 an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced…
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…
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…
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…
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 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…
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…
Kernelization is the standard framework to analyze preprocessing routines mathematically. Here, in terms of efficiency, we demand the preprocessing routine to run in time polynomial in the input size. However, today, various NP-complete…
A polynomial Turing kernel for some parameterized problem $P$ is a polynomial-time algorithm that solves $P$ using queries to an oracle of $P$ whose sizes are upper-bounded by some polynomial in the parameter. Here the term "polynomial"…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. In the aspect of kernelization, an impressive hardness theory has been established [Bodlaender etc. (ICALP 2008,…
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…
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…
We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…
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…
A parameterized problem consists of a classical problem and an additional component, the so-called parameter. This point of view allows a formal definition of preprocessing: Given a parameterized instance (I,k), a polynomial kernelization…