# Sparsification and subexponential approximation

@article{Bonnet2016SparsificationAS, title={Sparsification and subexponential approximation}, author={{\'E}douard Bonnet and Vangelis Th. Paschos}, journal={Acta Informatica}, year={2016}, volume={55}, pages={1-15} }

Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time approximation. We develop a new tool for inapproximability, called approximation preserving sparsification, and use it in order to get strong inapproximability results in subexponential time for several fundamental optimization problems such as min dominating set…

## 9 Citations

### Positive and Negative Results in Approximation and Parameterized Complexity

- Computer Science, Mathematics
- 2014

This thesis presents a new technique called greediness-For-Parameterization and it is used to improve the parameterized complexity of many problems and to obtain parameterized algorithms for some problems in bipartite graphs.

### On subexponential running times for approximating directed Steiner tree and related problems

- Mathematics, Computer ScienceArXiv
- 2018

Almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems, are proved by proving (1-d)ln n approximation algorithms for all these problems that run in time 2^{n^{d \log n } poly(m).

### Lower Bounds for the Parameterized Complexity of Minimum Fill-in and Other Completion Problems

- Mathematics, Computer ScienceSODA
- 2016

The second result proves that a significant improvement of any of these algorithms would lead to a surprising breakthrough in the design of approximation algorithms for MIN BISECTION, as well as improved, yet still not tight, lower bounds for FEEDBACK ARC SET in TOURNAMENTS.

### Maximization Problems Parameterized Using Their Minimization Versions: The Case of Vertex Cover

- Computer ScienceArXiv
- 2015

The main contribution is a parameterized approximation algorithm forMMVC, including its weighted variant, which gives conditional lower bounds for the running times of algorithms for MMVC and its weighted variants.

### Kernelization of Maximum Minimal Vertex Cover

- Mathematics, Computer Science
- 2021

It is proved that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover, even on bipartite graphs, unless NP ⊆ coNP/poly, unless P = NP, if the kernelization algorithms to apply only a type of natural reduction rules that are large optimal preserving rules.

### A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover

- Computer Science, MathematicsIPEC
- 2021

It is proved that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover of the input graph, even on bipartite graphs, unless NP ⊆ coNP / poly .

### New Tools and Connections for Exponential-Time Approximation

- Mathematics, Computer ScienceAlgorithmica
- 2018

A sparsification procedure that reduces a problem to a bounded-degree variant, allowing the use of approximation algorithms for bounded- degree graphs, and a connection between PCP parameters and exponential-time approximation algorithms is shown.

### Introducing lop-kernels: a framework for kernelization lower bounds

- Computer Science, MathematicsAlgorithmica
- 2022

It is shown that the trivial quadratic kernel for MMVC is essentially optimal, answering a question of Boria et al.

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