DeepAI

# On the Approximate Compressibility of Connected Vertex Cover

The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive attention in various subdomains of algorithmics. In the area of kernelization, it is known that this problem is unlikely to have efficient preprocessing algorithms, also known as polynomial kernelizations. However, it has been shown in a recent work of Lokshtanov et al. [STOC 2017] that if one considered an appropriate notion of approximate kernelization, then this problem parameterized by the solution size does admit an approximate polynomial kernelization. In fact, Lokhtanov et al. were able to obtain a polynomial size approximate kernelization scheme (PSAKS) for Connected Vertex Cover parameterized by the solution size. A PSAKS is essentially a preprocessing algorithm whose error can be made arbitrarily close to 0. In this paper we revisit this problem, and consider parameters that are strictly smaller than the size of the solution and obtain the first polynomial size approximate kernelization schemes for the Connected Vertex Cover problem when parameterized by the deletion distance of the input graph to the class of cographs, the class of bounded treewidth graphs, and the class of all chordal graphs.

• 12 publications
• 11 publications
• 59 publications
11/21/2017

### Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels

The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph th...
04/27/2020

### Approximate Turing Kernelization for Problems Parameterized by Treewidth

We extend the notion of lossy kernelization, introduced by Lokshtanov et...
02/19/2023

### Parameterized Max Min Feedback Vertex Set

Given a graph G and an integer k, Max Min FVS asks whether there exists ...
05/16/2022

### A faster algorithm for Vertex Cover parameterized by solution size

We describe a new algorithm for vertex cover with runtime O^*(1.25400^k)...
06/08/2020

### Graph Minors Meet Machine Learning: the Power of Obstructions

Computational intractability has for decades motivated the development o...
10/13/2022

### On the Minimum Cycle Cover problem on graphs with bounded co-degeneracy

In 2021, Duarte, Oliveira, and Souza [MFCS 2021] showed some problems th...
09/06/2020

### On Hardness of Approximation of Parameterized Set Cover and Label Cover: Threshold Graphs from Error Correcting Codes

In the (k,h)-SetCover problem, we are given a collection 𝒮 of sets over ...