  Motivated by efforts to incorporate sheaves into networking, we seek to
reinterpret pathfinding algorithms in terms of cellular sheaves, using
Dijkstra's algorithm as an example. We construct sheaves on a graph with
distinguished source and sink vertices, in which paths are represented by
sections. The first sheaf is a very general construction that can be applied to
other algorithms, while the second is created specifically to capture the
decision making of Dijkstra's algorithm. In both cases, Dijkstra's algorithm
can be described as a systematic process of extending local sections to global
sections. We discuss the relationship between the two sheaves and summarize how
other pathfinding algorithms can be interpreted in a similar way. While the
sheaves presented here address paths and pathfinding algorithms, we suggest
that future work could explore connections to other concepts from graph theory
and other networking algorithms. This work was supported by the NASA Internship
Project and SCaN Internship Project during the summer of 2020.
