approximation algorithms

20
Approximation Algorithms Bin Packing

Upload: meira

Post on 09-Jan-2016

20 views

Category:

Documents


0 download

DESCRIPTION

Approximation Algorithms. Bin Packing. Definition. Theorem. An Easy Solution: First Fit. Asymptotic PTAS. Multiway Cut and k-Cut. Definition. Example. Can you prove it???. Approximation. Analysis. Minimum k-cut Problem. Example. Construct a Gomory-Hu Tree. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: Approximation Algorithms

Approximation Algorithms

Bin Packing

Page 2: Approximation Algorithms

My T. [email protected]

2

Definition

Page 3: Approximation Algorithms

My T. [email protected]

3

Theorem

Page 4: Approximation Algorithms

My T. [email protected]

4

An Easy Solution: First Fit

Page 5: Approximation Algorithms

My T. [email protected]

5

Asymptotic PTAS

Page 6: Approximation Algorithms

My T. [email protected]

6

Page 7: Approximation Algorithms

My T. [email protected]

7

Page 8: Approximation Algorithms

Multiway Cut and k-Cut

My T. [email protected]

8

Page 9: Approximation Algorithms

Definition

My T. [email protected]

9

Page 10: Approximation Algorithms

Example

My T. [email protected]

10

Page 11: Approximation Algorithms

My T. [email protected]

11

Can you prove it???

Page 12: Approximation Algorithms

Approximation

My T. [email protected]

12

Page 13: Approximation Algorithms

Analysis

My T. [email protected]

13

Page 14: Approximation Algorithms

Minimum k-cut Problem

My T. [email protected]

14

Page 15: Approximation Algorithms

Example

My T. [email protected]

15

Page 16: Approximation Algorithms

Construct a Gomory-Hu Tree

My T. [email protected]

16

Page 17: Approximation Algorithms

My T. [email protected]

17

Page 18: Approximation Algorithms

Properties of Gomory-Hu Tree wrt k-cut

My T. [email protected]

18

Page 19: Approximation Algorithms

Approximation Algorithm

My T. [email protected]

19

Page 20: Approximation Algorithms

Analysis

My T. [email protected]

20