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PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 1: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,
Page 2: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

o

o

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2

Page 3: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 4: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 5: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 6: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 7: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 8: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 9: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

o 𝑑4𝑑

o 4𝑑𝑑

9

Page 10: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 11: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 12: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 13: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 14: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 15: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

• 𝑏

𝑑 σ𝑖=1𝑑 𝑏𝑖 = Θ 𝑏𝑑

15

Θ 𝑏𝑑 Θ 𝑏𝑑

Page 16: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

1. Θ(𝑏 ⋅ 𝑑)

2. Θ((𝑏/2)𝑑)

3. Θ(𝑏𝑑/2)

4. Θ(𝑏𝑑)

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Page 17: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

𝑔(𝑛)

𝑔(𝑛)

o

o

17

Page 18: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

• 𝜖 > 0

• 𝐶∗

𝜖1 + ⌊𝐶∗/𝜖⌋

• Θ(𝑏𝑑+1)

18

Θ 𝑏1+ 𝐶∗/𝜖 Θ 𝑏1+ 𝐶∗/𝜖

Page 19: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 20: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 21: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Θ 𝑏𝑚 Θ 𝑏 ⋅ 𝑚

Page 22: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

• Θ 𝑏𝑚 𝑚

22

Θ 𝑏𝑚 Θ 𝑏 ⋅ 𝑚

Page 23: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

• ℓ = 1,2,…

𝑑 ⋅ 𝑏 + 𝑑 − 1 𝑏2 +⋯+ 1 ⋅ 𝑏𝑑 = Θ 𝑏𝑑

23

Θ 𝑏𝑑 Θ 𝑏 ⋅ 𝑑

Page 24: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Θ 𝑏𝑑 Θ 𝑏𝑑

Θ 𝑏1+ 𝐶∗/𝜖 Θ 𝑏1+ 𝐶∗/𝜖

Θ 𝑏𝑚 Θ 𝑏 ⋅ 𝑚

Θ 𝑏𝑑 Θ 𝑏 ⋅ 𝑑

Page 25: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 26: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 27: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 28: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 29: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

o ≈

o

o

o

o

o

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Page 30: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 31: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 32: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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Page 33: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,
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Page 35: PowerPoint Presentationarielpro/15381f16/slides/781f16-2.pdfMicrosoft, Albuquemue, New Mexico Christos H. PAPADIMITRIOU*t Depanment of Electrical Engineenng, University of California,

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