Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Finding Minimal Forbidden Minors Using a Finite Congruence
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Safe Reduction Rules for Weighted Treewidth
Algorithmica
Invitation to data reduction and problem kernelization
ACM SIGACT News
On problems without polynomial kernels
Journal of Computer and System Sciences
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On the hardness of losing width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
Clique cover and graph separation: new incompressibility results
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Kernel bounds for structural parameterizations of pathwidth
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
European Journal of Combinatorics
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
TREEWIDTH and PATHWIDTH parameterized by the vertex cover number
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
On the Hardness of Losing Width
Theory of Computing Systems
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Using the framework of kernelization we study whether efficient preprocessing schemes for the Treewidth problem can give provable bounds on the size of the processed instances. Assuming the AND-distillation conjecture to hold, the standard parameterization of Treewidth does not have a kernel of polynomial size and thus instances (G, k) of the decision problem of Treewidth cannot be efficiently reduced to equivalent instances of size polynomial in k. In this paper, we consider different parameterizations of Treewidth. We show that Treewidth has a kernel with O(l3) vertices, where l denotes the size of a vertex cover, and a kernel with O(l4) vertices, where l denotes the size of a feedback vertex set. This implies that given an instance (G, k) of Treewidth we can efficiently reduce its size to O((l*)4) vertices, where l* is the size of a minimum feedback vertex set in G. In contrast, we show that Treewidth parameterized by the vertex-deletion distance to a co-cluster graph and Weighted Treewidth parameterized by the size of a vertex cover do not have polynomial kernels unless NP ⊆ coNP/poly. Treewidth parameterized by the target value plus the deletion distance to a cluster graph has no polynomial kernel unless the AND-distillation conjecture does not hold.