Questions tagged [kernelization]

Questions related to the existence of kernels for parameterized problems.

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Is the reduction from a parametrized proplem to the problem kernel just a kind of Karp reduction (polynomial-time reduction)?

The kernel of a parameterized problem $L$ is a reduction $(x,k) \mapsto (x',k')$ such that: $(x,k) \in L \Leftrightarrow (x',k') \in L$ $|x'| \leq f(k)$ for some function $f$ $k' \leq g(k)$ for some ...
11
votes
2answers
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Major open problems on polynomial kernel (non) existence

We are not able to settle the (non-)existence of a polynomial kernel for a parameterized combinatorial NP-complete problem (we also tried to apply some recent lower bound techniques to prove the non-...
7
votes
0answers
229 views

Can we achieve a better kernel for the Vertex Cover problem on planar graphs?

We have known how to get a $2k$ kernel for the Vertex Cover problem for thirty years, and it is not expected to be improved assuming UGC. My question is, can we do better for planar graphs? It is easy ...