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Minimum spanning tree

Minimum spanning tree. Prof Amir Geva Eitan Netzer. Definition. A sub group of edges from weighted graph G Spanning – reach all vertex Minimal – the sum of its edges is the lowest of all spanning trees Uses – connect a network with while spending minimum money

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Minimum spanning tree

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  1. Minimum spanning tree Prof Amir Geva Eitan Netzer

  2. Definition A sub group of edges from weighted graph G • Spanning – reach all vertex • Minimal – the sum of its edges is the lowest of all spanning trees • Uses – connect a network with while spending minimum money • Graph need to be connective

  3. Prim algorithm (1957) • Greedy algorithm • Start with an empty list of vertex. • Choose starting vertex from G. Randomly or a given choice. • Add edge with minimal weight that not used yet to an un explored vertex. • Continue until list of vertex contain all vertex in G.

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  5. Kruskal'salgorithm (1956) • Greedy algorithm • Create a “forest” F a set of trees • Create a set S containing all edges of G • While S is not empty and F is not a spanning tree yet • Remove minimum edge from S • If edge connects to trees in F combine them • Else discard edge

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