相关论文: Clique cover and graph separation: New incompressi…
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…
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 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"…
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…
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,…
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…
We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the…
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…
We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial…
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…
We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an…
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…
Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…
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…
In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is…
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…
The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However, there are…
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…
We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L AND/OR-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…