End of Term Review 2.9

End of Term Review 2.9 - Example 2. Single-Source Shortest...

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Unformatted text preview: Example 2. Single-Source Shortest Path on a General Graph (May Contain Cycles) This is fundamentally harder, because the first paths we discover may not be the shortest (not monotonic). CSE 2011 Prof. J. Elder - 91 - Last Updated: 4/1/10 2:37 PM Dijkstra’s Algorithm: Operation We grow a “cloud” S of vertices, beginning with s and eventually covering all the vertices We store with each vertex v a label d(v) representing the distance of v from s in the subgraph consisting of the cloud S and its adjacent vertices At each step We add to the cloud S the vertex u outside the cloud with the smallest distance label, d(u) We update the labels of the vertices adjacent to u s 9 S 1 7 CSE 2011 Prof. J. Elder - 92 - 4 11 Last Updated: 4/1/10 2:37 PM Dijkstra’s algorithm: Analysis Analysis: Using minheap, queue operations takes O(logV) time CSE 2011 Prof. J. Elder - 93 - Last Updated: 4/1/10 2:37 PM Example CSE 2011 Prof. J. Elder Key: White Grey Black - 94 - Vertex Q = V - S Vertex = min(Q) Vertex S, Off Queue Last Updated: 4/1/10 2:37 PM Example CSE 2011 Prof. J. Elder - 95 - Last Updated: 4/1/10 2:37 PM ...
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End of Term Review 2.9 - Example 2. Single-Source Shortest...

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