Stefan Kratsch

TL;DR: In this paper, the authors introduce the cross-composition framework for proving kernelization lower bounds, which generalizes and strengthens the recent techniques of using composition algorithms and of transferring the lower bounds via polynomial parameter transformations.

TL;DR: This work applies the representative sets tool to the problem of finding irrelevant vertices in graph cut problems, that is, vertices which can be made undeletable without affecting the status of the problem, and gives the first significant progress towards a polynomial kernel for the Multiway Cut problem.

TL;DR: It is shown that if an NP-hard problem cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless thePolynomial hierarchy collapses, and its applicability is shown by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations.

TL;DR: It is shown, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in unary encoding), that this running time cannot be improved to f(k)@?n^O^(^1^) for any function f( k) (under standard complexity assumptions).