DeepAI
Log In Sign Up

Edge Augmentation with Controllability Constraints in Directed Laplacian Networks

05/13/2021
by   Waseem Abbas, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/03/2022

Matching Augmentation via Simultaneous Contractions

We consider the matching augmentation problem (MAP), where a matching of...
09/01/2022

Diameter Minimization by Shortcutting with Degree Constraints

We consider the problem of adding a fixed number of new edges to an undi...
05/21/2015

Inferring Graphs from Cascades: A Sparse Recovery Framework

In the Network Inference problem, one seeks to recover the edges of an u...
08/25/2022

Edge-coloured graph homomorphisms, paths, and duality

We present a edge-coloured analogue of the duality theorem for transitiv...
07/12/2022

Edge Augmentation on Disconnected Graphs via Eigenvalue Elevation

The graph-theoretical task of determining most likely inter-community ed...
09/10/2019

Electrical Flows over Spanning Trees

This is the first paper to give provable approximation guarantees for th...
02/28/2021

Criminal Networks Analysis in Missing Data scenarios through Graph Distances

Data collected in criminal investigations may suffer from: (i) incomplet...