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Problem � Find a low cost network connecting a set of locations � Any pair of locations are connected � There is no cycle � Some applications: � Communication networks � Circuit design � … My T. Thai mythai@cise.ufl.edu 2
Minimum Spanning Tree (MST) Problem � Input: Undirected, connected graph G=(V, E), each edge (u, v) E has weight w(u, v) � Output: acyclic subset T E that connects all of the vertices with minimum total weight w(T) = (u,v) T w(u,v) My T. Thai mythai@cise.ufl.edu Bold edges form a Minimum Spanning Tree 3
Page 1: Introduction to Algorithms Minimum
Page 6 and 7: Some definitions � An edge is a l
Page 8 and 9: Corollary � In GENERIC-MST � A
Page 10 and 11: Disjoint-set data structure � Mai
Page 12 and 13: Example My T. Thai mythai@cise.ufl.
Page 14 and 15: Prim’s Algorithm � Builds one t
Page 16 and 17: Running time: O(E lgV) � Using bi
Page 18 and 19: My T. Thai mythai@cise.ufl.edu 18
Page 20: Summary � Prim’s algorithm star

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