# Partial containment control over signed graphs

## TL;DR

This paper addresses the challenge of containment control in signed networks with antagonistic interactions, proposing an efficient node selection method to maximize containment under control constraints.

## Contribution

It introduces a graph condensation-based approach and formulates an integer linear problem for optimal node control selection in constrained containment scenarios.

## Key findings

- The proposed method effectively maximizes containment with limited control signals.
- Simulation results demonstrate the efficiency and effectiveness of the node selection strategy.

## Abstract

In this paper, we deal with the containment control problem in presence of antagonistic interactions. In particular, we focus on the cases in which it is not possible to contain the entire network due to a constrained number of control signals. In this scenario, we study the problem of selecting the nodes where control signals have to be injected to maximize the number of contained nodes. Leveraging graph condensations, we find a suboptimal and computationally efficient solution to this problem, which can be implemented by solving an integer linear problem. The effectiveness of the selection strategy is illustrated through representative simulations.