Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Densest $k$-Connected Subgraphs   Dense subgraph discovery is an important graph-mining primitive with a
variety of real-world applications. One of the most well-studied optimization
problems for dense subgraph discovery is the densest subgraph problem, where
given an edge-weighted undirected graph $G=(V,E,w)$, we are asked to find
$S\subseteq V$ that maximizes the density $d(S)$, i.e., half the weighted
average degree of the induced subgraph $G[S]$. This problem can be solved
exactly in polynomial time and well-approximately in almost linear time.
However, a densest subgraph has a structural drawback, namely, the subgraph may
not be robust to vertex/edge failure. Indeed, a densest subgraph may not be
well-connected, which implies that the subgraph may be disconnected by removing
only a few vertices/edges within it. In this paper, we provide an algorithmic
framework to find a dense subgraph that is well-connected in terms of
vertex/edge connectivity. Specifically, we introduce the following problems:
given a graph $G=(V,E,w)$ and a positive integer/real $k$, we are asked to find
$S\subseteq V$ that maximizes the density $d(S)$ under the constraint that
$G[S]$ is $k$-vertex/edge-connected. For both problems, we propose
polynomial-time (bicriteria and ordinary) approximation algorithms, using
classic Mader's theorem in graph theory and its extensions.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess