next up previous
Next: Pseudocode Up: CSE 2320: Algorithms and Previous: Example: Professor Bumstead gets

Strongly Connected Components

Many graph applications look for a minimal way to connect each vertex to every other vertex.

Examples: bridging gaps, identifying bottlenecks



\psfig{figure=figures/f16-14.ps}

A graph G = (V, E) is if for every pair of vertices <u,v>, u,v $\in$ V, there is a path ($\leadsto$) from u to v (u $\leadsto$ v) and from v to u (v $\leadsto$ u).

A (SCC) of a graph G = (V, E) is a maximal set U $\subseteq$ V such that for every pair <u,v>$\in$ U, u $\leadsto$ v and v $\leadsto$ u.

Define: The of graph G = (V, E) is the graph \(G^T \;=\; (V, \;E^T)\), where \(E^T \;=\;\{(u,v) \;\mid\; (v,u) \;\in\; E\}\).

Time to create GT = O(V+E)



Copyright © 1998 The University of Texas at Arlington