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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 Gpred is a shortest path from s to v in G.



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


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