Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully Dynamic Algorithm for Top-$k$ Densest Subgraphs   Given a large graph, the densest-subgraph problem asks to find a subgraph
with maximum average degree. When considering the top-$k$ version of this
problem, a na\"ive solution is to iteratively find the densest subgraph and
remove it in each iteration. However, such a solution is impractical due to
high processing cost. The problem is further complicated when dealing with
dynamic graphs, since adding or removing an edge requires re-running the
algorithm. In this paper, we study the top-$k$ densest-subgraph problem in the
sliding-window model and propose an efficient fully-dynamic algorithm. The
input of our algorithm consists of an edge stream, and the goal is to find the
node-disjoint subgraphs that maximize the sum of their densities. In contrast
to existing state-of-the-art solutions that require iterating over the entire
graph upon any update, our algorithm profits from the observation that updates
only affect a limited region of the graph. Therefore, the top-$k$ densest
subgraphs are maintained by only applying local updates. We provide a
theoretical analysis of the proposed algorithm and show empirically that the
algorithm often generates denser subgraphs than state-of-the-art competitors.
Experiments show an improvement in efficiency of up to five orders of magnitude
compared to state-of-the-art solutions.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics