Transcription of Lecture 7: Minimum Spanning Trees and Prim’s Algorithm
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Lecture7:MinimumSpanningTreesandPrim s AlgorithmCLRSC hapter23 OutlineofthisLecture Spanningtreesandminimumspanningtrees. Theminimumspanningtree(MST)problem. Thegeneric algorithmforMSTproblem. Prim s algorithmfortheMSTproblem. Thealgorithm Correctness Implementation+ RunningTime1 SpanningTreesSpanningTrees:Asubgraph of a undirectedgraph is aspanningtreeof if it is a treeandcontainsevery vertex of .Example: abcdeabcdeabcdeabcdeGraphspanningtree1sp anningtree2spanningtree32 SpanningTreesTheorem:Every connectedgraphhasa :Why is thistrue?Question:Givena connectedgraph , how canyoufinda spanningtreeof ?3 WeightedGraphsWeightedGraphs:A weightedgraphis a graph,inwhicheachedgehasa weight(somerealnumber).
The minimum spanning tree (MST) problem. The generic algorithm for MST problem. Prim’s algorithm for the MST problem. – The algorithm – Correctness – Implementation + Running Time 1. Spanning Trees Spanning Trees: A subgraph of …
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