# Introduction to All-Pairs Shortest Paths

Learn about the history and evolution of all-pairs shortest paths algorithms.

## Shortest path tree

Previously, we discussed several algorithms to find the shortest paths from a single source vertex $s$ to every other vertex of the graph by constructing the shortest path tree rooted at $s$. The shortest path tree specifies two pieces of information for each node $v$ in the graph:

- $dist(v)$ is the length of the shortest path from $s$ to $v$.
- $pred(v)$ is the second-to-last vertex in the shortest path from $s$ to $v$.

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