PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j...
Transcript of PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j...
![Page 1: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/1.jpg)
![Page 2: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/2.jpg)
![Page 3: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/3.jpg)
![Page 4: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/4.jpg)
![Page 5: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/5.jpg)
![Page 6: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/6.jpg)
![Page 7: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/7.jpg)
![Page 8: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/8.jpg)
x y
x y
I t i i
i i x y N x yI x y t
i ii i x y N x y
I x y t
1 11
I I Iu v
x y t
n nn
I I Iu v
x y t
![Page 9: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/9.jpg)
I t i i
i i x y N x yI x y t
i ii i x y N x y
I x y t
1 11
I I Iu v
x y t
n nn
I I Iu v
x y t
![Page 10: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/10.jpg)
I t i i
i i x y N x yI x y t
i ii i x y N x y
I x y t
1 11
I I Iu v
x y t
n nn
I I Iu v
x y t
![Page 11: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/11.jpg)
x i j y i j ti j i ji jI u I v I
i j
![Page 12: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/12.jpg)
x i j y i j ti j i ji jI u I v I
2 2 2 2
1 1 1 1i j i j i j i j i j i j i j i ju u u u u u u u
i j
2 2 2 2
1 1 1 1i j i j i j i j i j i j i j i jv v v v v v v v
![Page 13: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/13.jpg)
x i j y i j ti j i ji jI u I v I
2u
i j
2v
![Page 14: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/14.jpg)
i j
2 22
minimizei j i j
x i j y i j t i j i ju v
i j
I u I v I u v
![Page 15: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/15.jpg)
i j
2 22
minimizei j i j
x i j y i j t i j i ju v
i j
I u I v I u v
i j i ju v
2 0x x i j y i j t i j
I I u I v I u
2 0y x i j y i j t i j
I I u I v I v
2 22
2 2x y
![Page 16: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/16.jpg)
2 2
2 2
G G G GG
u v u v
i j
![Page 17: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/17.jpg)
i j
2 22
minimizei j i j
x i j y i j t i j i ju v
i j
I u I v I u v
i j i ju v
2 0x x i j y i j t i j
I I u I v I u
2 0y x i j y i j t i j
I I u I v I v
2 22
2 2
u uu
x y
1 1 1 1
1
4i j i j i j i j i j
u u u u u
![Page 18: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/18.jpg)
i j
2 22
minimizei j i j
x i j y i j t i j i ju v
i j
I u I v I u v
i j i ju v
2 0x x i j y i j t i j
I I u I v I u
2 0y x i j y i j t i j
I I u I v I v
2 22
2 2
u uu
x y
i j i j
u u
![Page 19: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/19.jpg)
i j
0x x i j y i j t i j i j
I I u I v I u u
0y x i j y i j t i j i j
I I u I v I v v
![Page 20: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/20.jpg)
i j
0x x i j y i j t i j i j
I I u I v I u u
0y x i j y i j t i j i j
I I u I v I v v
2
2
x i j x y i j i j x t
x y i j y i j i j y t
I u I I v u I I
I I u I v v I I
![Page 21: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/21.jpg)
i j
0x x i j y i j t i j i j
I I u I v I u u
0y x i j y i j t i j i j
I I u I v I v v
2
2
x i j x y i j i j x t
x y i j y i j i j y t
I u I I v u I I
I I u I v v I I
![Page 22: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/22.jpg)
i j
0x x i j y i j t i j i j
I I u I v I u u
0y x i j y i j t i j i j
I I u I v I v v
2
2
x i j x y i j i j x t
x y i j y i j i j y t
I u I I v u I I
I I u I v v I I
i j i ju v
![Page 23: PowerPoint Presentationhspark/csci5561_S2020/Lec... · 2020. 1. 20. · ij I I u I v I u u x x i j y i j t i j i j O 00 vj O 2 2 t t I I OO OO 1 22 1 22 kk kkx x i j y i j t i j i](https://reader036.fdocuments.es/reader036/viewer/2022062307/5fdfaf2a3ee30437e40d6ae6/html5/thumbnails/23.jpg)
i j
0x x i j y i j t i j i j
I I u I v I u u
0y x i j y i j t i j i j
I I u I v I v v
2
2
x i j x y i j i j x t
x y i j y i j i j y t
I u I I v u I I
I I u I v v I I
1
2 2
1
2 2
k k
x x i j y i j tk k
i j i j
x y
k k
y x i j y i j tk k
i j i j
x y
I I u I v Iu u
I I
I I u I v Iv v
I I