# Computational Approaches for Zero Forcing and Related Problems

## TL;DR

This paper introduces new computational methods combining integer programming and combinatorial algorithms to solve zero forcing problems and their variants more efficiently than existing approaches.

## Contribution

It presents the first general-purpose algorithms for connected zero forcing and controlling forcing timesteps, outperforming brute force methods.

## Key findings

- Algorithms are competitive with state-of-the-art zero forcing methods.
- Proposed methods outperform brute force approaches.
- New formulations for zero forcing as dynamic and set-covering problems.

## Abstract

In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of timesteps. Our approaches are based on a combination of integer programming models and combinatorial algorithms, and include formulations for zero forcing as a dynamic process, and as a set-covering problem. We explore several solution strategies for these models, test them on various types of graphs, and show that they are competitive with the state-of-the-art algorithm for zero forcing. Our proposed algorithms for connected zero forcing and for controlling the number of zero forcing timesteps are the first general-purpose computational methods for these problems, and are superior to brute force computation.