Kernels for packing and covering problems

TL;DR: In this paper , the authors surveyed a tool called expansion lemma, which helps in reducing the size of the kernel of a fixed-parameter tractable problem with polynomial-sized kernels.

TL;DR: This paper introduces approximation algorithms for the directed k-path partition problem, a variant of the k-path partition problem on digraphs, with applications in facility location, network monitoring, and transportation networks, achieving improved ratios for k≥3.

TL;DR: The balanced crown decomposition as discussed by the authors is a combination of a crown-decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems.

TL;DR: The study of its kernelization algorithms is continued, and a $5k$-vertex kernel is developed that addresses the problem of whether a graph contains vertex-disjoint paths each of length two.

TL;DR: This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research.

TL;DR: Using the notion of distillation algorithms, a generic lower-bound engine is developed that allows showing that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomially-bounded hierarchy collapses.

TL;DR: The problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in 0( 4’( k + 1) --3’2 (m + n) ) time, and is thus fixed-parameter tractable.

TL;DR: It is argued that simulations fundamentally differ from experiments with regard to the background knowledge that is invoked to argue for the “external validity” of the investigation.