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# 18 - CS 323/700 Lecture 18 Design and Analysis of...

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n CS 323/700 ± ± Lecture 18 o Design and Analysis of Algorithms Hoeteck Wee · [email protected] http://algorithms.qwriting.org/

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Minimum cut Deﬁnitions 1. Cut: set of edges whose removal render the graph disconnected 2. Minimum cut: cut of the smallest size (size = # edges in the cut) @ @ @ @ @ @ b b b b 1 2 4 3 I cut: { ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) } h{ 1 } , { 2 , 3 , 4 }i I min-cut: { ( 1 , 4 ) , ( 3 , 4 ) 1 , 2 , 3 } , { 4 or { ( 1 , 2 ) , ( 2 , 3 ) 1 , 3 , 4 } , { 2 Easy Fact The minimum cut has size at most the minimum degree of any node. Hoeteck Wee CS 323/700 Apr 28, 2010 2 / 1
Minimum cut Deﬁnitions 1. Cut: set of edges whose removal render the graph disconnected 2. Minimum cut: cut of the smallest size (size = # edges in the cut) Minimum Cut Problem On input an undirected graph with n vertices, output a minimum cut. Applications I network reliability (nodes = machines, edges = connections) I clustering webpages (nodes = webpages, edges = hyperlinks) Hoeteck Wee CS 323/700 Apr 28, 2010 3 / 1

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Minimum cut Deﬁnitions 1. Cut: set of edges whose removal render the graph disconnected 2.
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18 - CS 323/700 Lecture 18 Design and Analysis of...

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