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Approximation Algorithms k-Center

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Approximation Algorithms. k-Center. Definition. ≤. 2-Approx. Analysis. Obtain Better Ratio?. Weighted k-Center. Notations. Algorithm. Algorithm 2. Analysis. Theorem: Alg 2 has an approx ratio of 3. Multiway Cut and k-Cut. Definition. Example. Can you prove it???. Approximation. - PowerPoint PPT Presentation

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Page 1: Approximation Algorithms

Approximation Algorithms

k-Center

Page 2: Approximation Algorithms

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Definition

≤

Page 3: Approximation Algorithms

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3

2-Approx

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Analysis

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Obtain Better Ratio?

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Weighted k-Center

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Notations

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Algorithm

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Algorithm 2

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Analysis

Theorem: Alg 2 has an approx ratio of 3.

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Multiway Cut and k-Cut

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Definition

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Page 15: Approximation Algorithms

Example

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Can you prove it???

Page 17: Approximation Algorithms

Approximation

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Analysis

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Minimum k-cut Problem

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Example

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Construct a Gomory-Hu Tree

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Properties of Gomory-Hu Tree wrt k-cut

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Approximation Algorithm

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Analysis

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