## 10 Citations

### Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

- Mathematics, Computer ScienceICALP
- 2013

It is shown that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H.

### Excluded Forest Minors and the Erdős–Pósa Property

- MathematicsCombinatorics, Probability and Computing
- 2013

It is shown that the function f can be taken to be linear when H is a forest, best possible in the sense that no linear bound is possible if H has a cycle.

### A Naive Algorithm for Feedback Vertex Set

- MathematicsSOSA
- 2018

It is shown that a greedy branching algorithm, which always branches on an undecided vertex with the largest degree, runs in single-exponential time, i.e., $O(c^k\cdot n^2)$ for some constant $c$.

### Quick but Odd Growth of Cacti

- MathematicsAlgorithmica
- 2017

Let $${\mathcal {F}}$$F be a family of graphs. Given an n-vertex input graph G and a positive integer k, testing whether G has a vertex subset S of size at most k, such that $$G-S$$G-S belongs to…

### Hitting minors on bounded treewidth graphs. I. General upper bounds

- MathematicsSIAM J. Discret. Math.
- 2020

For a finite collection of graphs, given a graph G and an integer k, deciding whether there exists S \subseteq V(G) with |S| with $|S| \leq... is the problem.

### Optimal Algorithms for Hitting (Topological) Minors on Graphs of Bounded Treewidth

- Mathematics, Computer ScienceIPEC
- 2017

It is proved that when all the graphs in ${\cal F}$ are connected and at least one of them is planar, then f_{{\cal F}}(w) = 2^{O (w \cdot\log w)}$.

### Hitting minors on bounded treewidth graphs.

- Mathematics
- 2017

The objective is to determine the smallest function $f_{{\cal F}}$ such that ${\cal F}$-M-Deletion can be solved in time, and to prove that it is 2^Theta(tw) for every collection of graphs.

### Some Contributions to Parameterized Complexity

- Economics
- 2018

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad, or from public or private research centers.

### Treewidth: algorithmic, combinatorial, and practical aspects

- Mathematics
- 2017

Dans cette these, nous etudions la complexite parametree de problemes combinatoires dans les graphes. Plus precisement, nous presentons une multitude d’algorithmes de programmation dynamique ainsi…

## References

SHOWING 1-10 OF 63 REFERENCES

### Planar F-Deletion: Approximation and Optimal FPT Algorithms

- Computer Science, MathematicsArXiv
- 2012

A randomized O(nm) time constant factor approximation algorithm for the optimization version of Planar F-Deletion and two FPT algorithms that unify, generalize, and improve over a multitude of results in the literature.

### Planar F-Deletion: Approximation, Kernelization and Optimal FPT Algorithms

- Computer Science, Mathematics2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

A number of generic algorithmic results about F-DELETION, when F contains at least one planar graph are obtained, which unify, generalize, and improve a multitude of results in the literature.

### An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem

- Computer Science, MathematicsTheory of Computing Systems
- 2007

It is proved that no FPT algorithm with a parameter function of the form O(2o(k)) is possible, unless there is an unlikely collapse of parameterized complexity classes, namely FPT = M[1].

### Hitting Forbidden Minors: Approximation and Kernelization

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2016

The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes, based on the results obtained on the F-Deletion problems.

### Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs

- MathematicsJACM
- 2005

We introduce a new framework for designing fixed-parameter algorithms with subexponential running time---2O(&kradic;) nO(1). Our results apply to a broad family of graph problems, called…

### Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 2006

### Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time

- Computer Science, Mathematics2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
- 2011

It is shown that the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing, and in several cases it is able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail.

### Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

- Mathematics, Computer ScienceICALP
- 2013

It is shown that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H.

### A Near-Optimal Planarization Algorithm

- Computer ScienceSODA
- 2014

A dynamic programming algorithm for Weighted Vertex Planarization on graphs of treewidth w with running time 2O(w log w) · n, thereby improving over previous double-exponential algorithms.

### Tight lower bounds for certain parameterized NP-hard problems

- Computer ScienceProceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
- 2004

It is proved that a group of parameterized NP-hard problems, including weighted SAT, dominating set, hitting set, set cover, and feature set, cannot be solved in time n/sup o(k)/poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size.