Bart M. P. Jansen

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

The aim of this article is to motivate and describe the parameter ecology program, which studies how different parameters contribute to the difficulty of classical problems. We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or polynomial kernels. An extensive overview of recent advances on this front is presented for the Vertex Cover problem. Moving even beyond the parameter ecology program we advocate the principle of model enrichment, which raises the challenge of generalizing positive results to problem definitions with greater modeling power. The computational intractability which inevitably emerges can be deconstructed by introducing additional parameters, leading towards a theory of fully multivariate algorithmics.

Preprocessing for Treewidth: A Combinatorial Analysis through 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 apply an array of preprocessing rules that simplify and shrink it. This work seeks to prove rigorous performance guarantees for such preprocessing rules---known rules as well as more recent ones---by studying them in the framework of kernelization from parameterized complexity. It is known that the NP-complete problem of determining whether a given graph

On polynomial kernels for structural parameterizations of odd cycle transversal

G

Parameterized complexity of vertex deletion into perfect graph classes

has treewidth at most

Kernel bounds for path and cycle problems

k

Turing kernelization for finding long paths and cycles in restricted graph classes

admits no polynomial-time preprocessing algorithm that reduces any input instance to size polynomial in

Preprocessing subgraph and minor problems: When does a small vertex cover help?

k

Approximation and kernelization for chordal vertex deletion

, unless NP

Connect the dot: Computing feed-links for network extension ∗

\subseteq

Polynomial kernels for hard problems on disk graphs

coNP/poly and the polynomial hierarchy collapses to its third level. In this paper we therefore consider structural graph measures larger than treewidth, and determine whether efficient preprocessing can shrink the instance size to a polynomial in such a parameter ...