Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discovering the structure of complex networks by minimizing cyclic
  bandwidth sum   Getting a labeling of vertices close to the structure of the graph has been
proved to be of interest in many applications e.g., to follow smooth signals
indexed by the vertices of the network. This question can be related to a graph
labeling problem known as the cyclic bandwidth sum problem. It consists in
finding a labeling of the vertices of an undirected and unweighted graph with
distinct integers such that the sum of (cyclic) difference of labels of
adjacent vertices is minimized. Although theoretical results exist that give
optimal value of cyclic bandwidth sum for standard graphs, there are neither
results in the general case, nor explicit methods to reach this optimal result.
In addition to this lack of theoretical knowledge, only a few methods have been
proposed to approximately solve this problem. In this paper, we introduce a new
heuristic to find an approximate solution for the cyclic bandwidth sum problem,
by following the structure of the graph. The heuristic is a two-step algorithm:
the first step consists of traversing the graph to find a set of paths which
follow the structure of the graph, using a similarity criterion based on the
Jaccard index to jump from one vertex to the next one. The second step is the
merging of all obtained paths, based on a greedy approach that extends a
partial solution by inserting a new path at the position that minimizes the
cyclic bandwidth sum. The effectiveness of the proposed heuristic, both in
terms of performance and time execution, is shown through experiments on graphs
whose optimal value of CBS is known as well as on real-world networks, where
the consistence between labeling and topology is highlighted. An extension to
weighted graphs is also proposed.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn