# Kernelization Lower Bounds Through Colors and IDs

@article{Dom2014KernelizationLB, title={Kernelization Lower Bounds Through Colors and IDs}, author={Michael Dom and Daniel Lokshtanov and Saket Saurabh}, journal={ACM Transactions on Algorithms (TALG)}, year={2014}, volume={11}, pages={1 - 20} }

In parameterized complexity, each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the nonexistence of polynomial kernels for specific problems has been developed by Bodlaender et al. [2009] and Fortnow and…

## 135 Citations

### Kernelization of packing problems

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### Tight Kernel Bounds for Problems on Graphs with Small Degeneracy

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- 2013

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### A ug 2 01 7 Diminishable Parameterized Problems and Strict Polynomial Kernelization

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### Optimal Sparsification for Some Binary CSPs Using Low- Degree Polynomials

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- 2016

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer, and characterize constraint types based on the minimum degree of multivariate polynomials whose roots correspond to the satisfying assignments.

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### Sparsification Upper and Lower Bounds for Graph Problems and Not-All-Equal SAT

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It is shown that for a number of decision problems on graphs, polynomial-time algorithms cannot compress instances of such problems to equivalent instances, of a possibly different problem, whose encoding size is sub-quadratic in the number of vertices.

### On the Approximate Compressibility of Connected Vertex Cover

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This paper considers parameters that are strictly smaller than the size of the solution and obtains the first polynomial size approximate kernelization schemes for the Connected Vertex Cover problem when parameterized by the deletion distance of the input graph.

### How Much Does a Treedepth Modulator Help to Obtain Polynomial Kernels Beyond Sparse Graphs?

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This article proves that Vertex Cover admits a polynomial kernel on general graphs for any integer c, and that Dominating Set does not for anyinteger $$c \ge 2$$c≥2 even on degenerate graphs, unless $$\text {NP} \subseteq \text {coNP}/\text{poly}$$NP⊆coNP/poly.

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