How can I avoid re-computation of Dijkstra algorithm if I add or remove one edge from a graph? I have a nested graph filtration and each step I have to find the shortest path between two nodes. At each step I just add one edge to the graph so the re-computation of the Dijkstra algorithm is extremely redundant. Is there any algorithm to circumvent this?
Pathfinding algorithms that are able to recompute the best path when the graph changes without doing a full recomputation are called "Incremental".

The incremental version of Dijkstra's algorithm has the horrible name DynamicSWSF-FP.

The much more common algorithm which combines this with A* is called LPA*