DAGs are crucial in computer science and AI for representing structures with dependencies among their elements, where some tasks must precede others. In AI, DAGs are often used to model problems that involve sequencing, scheduling, data processing pipelines, and the structures of neural networks, particularly in frameworks that require forward propagation without loops. They enable the representation of various processes and dependencies in a visual and mathematical manner, facilitating the understanding and optimization of complex systems. DAGs are particularly important in machine learning for constructing and training deep learning models, where the graph represents the flow of data and computations without cycles, ensuring that the feedforward and backpropagation algorithms can operate efficiently.

The concept of directed graphs has been part of mathematics and computer science since the mid-20th century, with the specific focus on acyclic properties to solve problems in scheduling, data processing, and more becoming prominent by the 1960s and 1970s.

While the development of DAGs as a concept is a collective advancement rooted in graph theory and computer science, no single individual is credited with their inception. Instead, they have been refined and applied by numerous scholars and practitioners across various fields, including computer science, mathematics, and operations research.