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Unformatted text preview: Lecture 27 CSE 331 Nov 2, 2010 Online Office Hr @ 10:00 10:30pm Follow the collaboration rules Write down names of your collaborators Collaboration is only until the proof idea stage Any deviations HW 7 onwards would be considered cheating Cut Property Lemma for MSTs S S V \ S V \ S Cheapest crossing edge is in all MSTs Condition: S and V\S are nonempty Assumption: All edge costs are distinct S S V \ S V \ S Optimality of Kruskal’s Algorithm Input: G=(V,E) , c e > 0 for every e in E T = Ø Sort edges in increasing order of their cost Consider edges in sorted order If an edge can be added to T without adding a cycle then add it to T S S Nodes connected to red in (V,T) Nodes connected to red in (V,T) S is nonempty V\S is nonempty First crossing edge considered Is (V,T) a spanning tree? No cycles by design Just need to show that (V,T) is connected S’ S’ V \ S’ V \ S’ No edges here No edges here G is disconnected! G is disconnected! Cut Property Lemma for MSTs S S V \ S V \ S Cheapest crossing edge is in all MSTs Condition: S and V\S are nonempty Optimality of Prim’s algorithm Input: G=(V,E) , c e > 0 for every e in...
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This note was uploaded on 12/11/2011 for the course CSE 331 taught by Professor Rudra during the Fall '11 term at SUNY Buffalo.
 Fall '11
 RUDRA

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