02-greedy

# 28 primsmstalgorithm greedy strategy choose some start

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Unformatted text preview: has the lowest weight of edges that… have one vertex in the tree and one not in the tree. Thus builds-up one tree by adding a new edge to it Can this lead (Tell me why not.) Is it optimal? (Yes. Need a proof.) 29 to an infeasible solution? Tracking Edges for Prim’s MST Candidates edges: edge from a tree-node to a non-tree node Since we’ll choose smallest, keep only one candidate edge for each non-tree node But, may need to make sure we always have the smallest edge for each non-tree node Fringe-nodes: non-trees nodes adjacent to the tree Need data structure to hold fringe-nodes Priority queue, ordered by min-edge weight May need to update priorities! 30 Prim’s Algorithm MST-Prim(G, wt) init PQ to be empty; PQ.Insert(s, wt=0); parent[s] = NULL; while (PQ not empty) v = PQ.ExtractMin(); for each w adj to v if (w is unseen) { PQ.Insert(w, wt(v,w)); parent[w] = v; } 31 else if (w is fringe &amp;&amp; wt[v,w] &lt; fringeWt(w)){ Cost of Prim’s Algorithm (Assume connected graph) Clearly it loo...
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## This note was uploaded on 02/25/2014 for the course CS 4102 taught by Professor Horton during the Spring '10 term at UVA.

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