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Shortest Paths Tree (single source)

Predecessor Subgraph $G_{pred} \;=\; (V_{pred}, \;E_{pred})$ for G = (V, E).

$\begin{displaymath}V_{pred} \;=\; \{v \in V \mid pred(v) \neq NIL\} \;\cup\; \{s\}\end{displaymath}$

$\begin{displaymath}E_{pred} \;=\; \{(pred(v), v) \in E \;\mid\; v \in V_{pred} \;-\; \{s\}\}\end{displaymath}$

The unique simple path from s to v in G_pred is a shortest path from s to v in G.

$\psfig{figure=figures/f18-2.ps}$

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