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Disjoint-set data structure � Maintain collection S = {S 1, . . . , S k} of disjoint dynamic (changing over time) sets � Each set is identified by a representative, which is some member of the set � Operations: � MAKE-SET(x): make a new set S i = {x}, and add S i to S � UNION(x, y): if x ∈ S x , y ∈ S y, then S ← S − S x − S y ∪ {S x ∪ S y} � Representative of new set is any member of S x ∪ S y, often the representative of one of S x and S y. � Destroys S x and S y (since sets must be disjoint). � FIND-SET(x): return representative of set containing x � In Kruskal’s Algorithm, each set is a connected component My T. Thai mythai@cise.ufl.edu 10
Pseudo code � Running time: O(E lg V) ( is E is sorted) � First for loop: |V| MAKE-SETs � Sort E: O(E lg E) - O(E lg V) � Second for loop: (o(E log V) (chapter 21) My T. Thai mythai@cise.ufl.edu 11
Page 1 and 2: Introduction to Algorithms Minimum
Page 3 and 4: Minimum Spanning Tree (MST) Problem
Page 6 and 7: Some definitions � An edge is a l
Page 8 and 9: Corollary � In GENERIC-MST � A
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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