We introduce the framework of cross-composition for proving kernelization lower bounds for a number of important graphs problems with structural (nonsta...Expand

We present two new approaches rooted in linear algebra, based on matrix rank and determinants, which provide deterministic c tw | V | O ( 1 ) time algorithms, also for weighted and counting versions of connectivity problems; we show how to evaluate those formulas via dynamic programming.Expand

We show how representative sets can be used to give a polynomial kernel for the elusive Almost 2-sat problem (where the task is to remove at most k clauses to make a 2-CNF formula satisfiable), solving a major open problem in kernelization.Expand

The framework of Bodlaender et al. (J Comput Sys Sci 75(8):423–434, 2009) and Fortnow and Santhanam allows us to exclude the existence of Turing kernels for a range of problems under reasonable complexity-theoretical assumptions.Expand

Given a graph G and an integer k, the ? Edge Completion/Editing/Deletion problem asks whether it is possible to add, edit, or delete at most k edges in G such that one obtains a graph that fulfills… Expand

We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in unary encoding), that the problem can be solved in time n^O^(^k^) for an input of length n by dynamic programming.Expand

We show that evolutionary algorithms solve the vertex cover problem efficiently if the size of a minimum vertex cover is not too large, i.e., the expected runtime is bounded by a function in the parameter.Expand