From Notices of the AMS
The Many Face(t)s of Zero Forcing
by Illya V. Hicks
Boris Brimkov
Introduction
What does getting good movie recommendations from Netflix have in common with monitoring the electrical power grid, searching for a fugitive who is trying to evade capture, and controlling a quantum system? All these tasks, and several others, can be modeled as the same graph optimization problem called zero forcing, and can be approached with the same battery of computational techniques. As an analogy, the zero forcing process can be thought of as a sudoku puzzle where through the limited information given, the rest of the missing information in the grid can be inferred. In this article, we outline several different settings where the zero forcing problem arose independently, and then discuss some of the solution techniques and remaining challenges related to the problem.
Zero forcing
We will begin with a purely graph-theoretic definition of zero forcing. Let $G=(V,E)$ be a graph and $S \subset V$ be a set of vertices initially colored blue, all other vertices being colored white.
- Also in Notices
- Compressed Sensing-based SARS-CoV-2 Pool Testing
- The Structure of Meaning in Language: Parallel Narratives in Linear Algebra and Category Theory
