Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph-based data clustering: a quadratic-vertex problem kernel for
  s-Plex Cluster Vertex Deletion   We introduce the s-Plex Cluster Vertex Deletion problem. Like the Cluster
Vertex Deletion problem, it is NP-hard and motivated by graph-based data
clustering. While the task in Cluster Vertex Deletion is to delete vertices
from a graph so that its connected components become cliques, the task in
s-Plex Cluster Vertex Deletion is to delete vertices from a graph so that its
connected components become s-plexes. An s-plex is a graph in which every
vertex is nonadjacent to at most s-1 other vertices; a clique is an 1-plex. In
contrast to Cluster Vertex Deletion, s-Plex Cluster Vertex Deletion allows to
balance the number of vertex deletions against the sizes and the density of the
resulting clusters, which are s-plexes instead of cliques. The focus of this
work is the development of provably efficient and effective data reduction
rules for s-Plex Cluster Vertex Deletion. In terms of fixed-parameter
algorithmics, these yield a so-called problem kernel. A similar problem, s-Plex
Editing, where the task is the insertion or the deletion of edges so that the
connected components of a graph become s-plexes, has also been studied in terms
of fixed-parameter algorithmics. Using the number of allowed graph
modifications as parameter, we expect typical parameter values for s-Plex
Cluster Vertex Deletion to be significantly lower than for s-Plex Editing,
because one vertex deletion can lead to a high number of edge deletions. This
holds out the prospect for faster fixed-parameter algorithms for s-Plex Cluster
Vertex Deletion.

2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg