Kruskal - Rediscovered by Sollin in 1960s 2 Prim’s...

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1 Spanning Tree Set of edges connecting all nodes in graph need N-1 edges for N nodes no cycles, can be thought of as a tree Can build tree during traversal
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2 Minimum Spanning Tree (MST) Spanning tree with minimum total edge weight
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3 Minimum Spanning Tree (MST) Possible to have multiple MSTs Different spanning trees with same weight Example applications Minimize length of telephone lines for neighborhood Minimize distance of airplane routes serving cities
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4 Algorithms for Finding MST Three well known algorithms 1. Borůvka’s algorithm [1926] For constructing efficient electricity network
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Unformatted text preview: Rediscovered by Sollin in 1960s 2. Prim’s algorithm [1957] First discovered by Vojtěch Jarník in 1930 Similar to Djikstra’s algorithm 3. Kruskal’s algorithm [1956] By Prof. Clyde Kruskal’s uncle 5 MST – Kruskal’s Algorithm sort edges by weight (from least to most) tree = for each edge (X,Y) in order if it does not create a cycle add (X,Y) to tree stop when tree has N–1 edges Keeps track of lightest edge remaining whether adding edge to MST creates cycle Optimal solution computed with greedy algorithm 6 MST – Kruskal’s Algorithm Example...
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Kruskal - Rediscovered by Sollin in 1960s 2 Prim’s...

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