Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge Augmentation with Controllability Constraints in Directed Laplacian
  Networks   In this paper, we study the maximum edge augmentation problem in directed
Laplacian networks to improve their robustness while preserving lower bounds on
their strong structural controllability (SSC). Since adding edges could
adversely impact network controllability, the main objective is to maximally
densify a given network by selectively adding missing edges while ensuring that
SSC of the network does not deteriorate beyond certain levels specified by the
SSC bounds. We consider two widely used bounds: first is based on the notion of
zero forcing (ZF), and the second relies on the distances between nodes in a
graph. We provide an edge augmentation algorithm that adds the maximum number
of edges in a graph while preserving the ZF-based SSC bound, and also derive a
closed-form expression for the exact number of edges added to the graph. Then,
we examine the edge augmentation problem while preserving the distance-based
bound and present a randomized algorithm that guarantees an approximate
solution with high probability. Finally, we numerically evaluate and compare
these edge augmentation solutions.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas