Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
On problems without polynomial kernels
Journal of Computer and System Sciences
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithmic meta-theorems for restrictions of treewidth
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
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
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
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
Kernel bounds for path and cycle problems
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
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Maximum common induced subgraph parameterized by vertex cover
Information Processing Letters
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We prove a number of results around kernelization of problems parameterized by a vertex cover of the input graph. We provide two simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like Odd Cycle Transversal, Chordal Deletion,η-Transversal, Long Path, Long Cycle, orH-packing, parameterized by the size of a vertex cover, they also imply new polynomial kernels for problems like $\mathcal{F}$-Minor-Free-Deletion, which is to delete at most k vertices to obtain a graph with no minor from a fixed finite set $\mathcal{F}$. While our characterization captures many interesting problems, the kernelization complexity landscape of problems parameterized by vertex cover is much more involved. We demonstrate this by several results about induced subgraph and minor containment, which we find surprising. While it was known that testing for an induced complete subgraph has no polynomial kernel unless NP ⊆ coNP/poly, we show that the problem of testing if a graph contains a complete graph on t vertices as a minor admits a polynomial kernel. On the other hand, it was known that testing for a path on t vertices as a minor admits a polynomial kernel, but we show that testing for containment of an induced path on t vertices is unlikely to admit a polynomial kernel.