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Sparsification Upper and Lower Bounds for Graph Problems and Not-All-Equal SAT
TLDR
It is proved that there is no polynomial-time algorithm that reduces any n-vertex input to an equivalent instance, of an arbitrary problem, with bitsize, and a non-trivial sparsification algorithm is exhibited for d-Not-All-Equal-SAT. Expand
Optimal Sparsification for Some Binary CSPs Using Low-degree Polynomials
TLDR
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. Expand
Sparsification Upper and Lower Bounds for Graphs Problems and Not-All-Equal SAT
TLDR
It is proved that there is no polynomial-time algorithm that reduces any n-vertex input to an equivalent instance, of an arbitrary problem, with bitsize O(n^{2-epsilon}) for epsilon > 0, unless NP is a subset of coNP/poly and the polynometric-time hierarchy collapses. Expand
Parameterized Complexity of Conflict-free Graph Coloring
TLDR
The NP-hard decision questions of whether for a constant q an input graph has a q-ONCF-coloring or aq-CNCF-coloration are studied, and the first upper bounds on $\chi_{ON}(G)$ with respect to minimum feedback vertex set size and treewidth are provided. Expand
Best-case and Worst-case Sparsifiability of Boolean CSPs
TLDR
A complete characterization of which constraint languages allow for a linear sparsification, including Boolean CSPs in which every constraint has arity at most three, and the optimal size of sparsifications in terms of the largest OR that can be expressed by the constraint language. Expand
Elimination Distances, Blocking Sets, and Kernels for Vertex Cover
TLDR
It is shown that in the most-studied setting, parameterized by the size of a deletion set to a specified graph class $\mathcal{C}$, bounded minimal blocking set size is necessary but not sufficient to get a polynomial kernelization. Expand
Optimal Data Reduction for Graph Coloring Using Low-Degree Polynomials
TLDR
The aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural properties, such as the size of a minimum vertex cover. Expand
Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations
TLDR
It is proved that for each set F of connected graphs and constant $\eta$, the F-Deletion problem parameterized by the size of a treedepth-one modulator has a polynomial kernel. Expand
Optimal Data Reduction for Graph Coloring Using Low-Degree Polynomials
TLDR
The aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural properties, such as the size of a minimum vertex cover. Expand
Optimal Sparsification for Some Binary CSPs Using Low-Degree Polynomials
TLDR
This article 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. Expand
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