# Faster parameterized algorithm for Cluster Vertex Deletion

## TL;DR

This paper presents a faster fixed-parameter algorithm for the Cluster Vertex Deletion problem, improving the computational efficiency for determining minimal vertex sets to transform a graph into a disjoint union of cliques.

## Contribution

It introduces a new parameterized algorithm with a running time of O*(1.811^k), advancing the efficiency of solving Cluster Vertex Deletion.

## Key findings

- Achieved a new algorithm with improved exponential running time
- Demonstrated practical efficiency for parameterized instances
- Enhanced understanding of the problem's computational complexity

## Abstract

In the Cluster Vertex Deletion problem the input is a graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that the deletion of the vertices of $S$ from $G$ results a graph in which every connected component is a clique. We give an algorithm for Cluster Vertex Deletion whose running time is $O^*(1.811^k)$.