CSE331 Lecture 25

CSE331 Lecture 25 - Kruskal’s Algorithm Joseph B. Kruskal...

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Lecture 25 CSE 331 Oct 28, 2011
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HW 6 due today Q1, Q2 and Q3 in separate piles I will not take any HW after 1:15pm
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Other HW related stuff HW 5 will be available for pickup from Monday Solutions to HW 6 at the end of the lecture HW 7 has been posted (link on the blog)
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Dijkstra’s shortest path algorithm Input: Directed G=(V,E) , l e ≥ 0 , s in V S = {s} , d(s) =0 While there is a v not in S with (u,v) in E , u in S Pick w that minimizes d’(w) Add w to S d(w) = d’(w) At most n iterations At most n iterations O(m) time O(m) time O(mn) time bound is trivial O(m log n) time implementation is possible d’(v) = min e=(u,v) in E , u in S d(u)+l e
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Reading Assignment Sec 4.4 of [KT]
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Building a fiber network Lay down fibers to connect n locations All n locations should be connected Laying down a fiber costs money What is the cheapest way to lay down the fibers?
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Today’s agenda Minimum Spanning Tree (MST) Problem Greedy algorithm(s) for MST problem
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HW 6 due today Q1, Q2 and Q3 in separate piles I will not take any HW after 1:15pm
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Unformatted text preview: Kruskal’s Algorithm Joseph B. Kruskal 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 Prim’s algorithm Robert Prim Similar to Dijkstra’s algorithm Input: G=(V,E) , c e > 0 for every e in E 2 1 3 51 50 0.5 S = {s}, T = Ø While S is not the same as V Among edges e= (u,w) with u in S and w not in S , pick one with minimum cost Add w to S , e to T 2 1 50 0.5 Reverse-Delete Algorithm Input: G=(V,E) , c e > 0 for every e in E T = E Sort edges in decreasing order of their cost Consider edges in sorted order If an edge can be removed T without disconnecting T then remove it 2 1 3 51 50 0.5 2 1 3 51 50 0.5 (Old) History of MST algorithms 1920: Otakar Borůvka 1930: Vojtěch Jarník 1956: Kruskal 1957: Prim 1959: Dijkstra Same algo! Same algo!...
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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.

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CSE331 Lecture 25 - Kruskal’s Algorithm Joseph B. Kruskal...

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