1. Matrices
An appeaser is one who feeds a crocodile—hoping it will eat him last.
Winston Churchhill

2. Types of Sparse Matrices
Random Distribution.

3. Types of Sparse Matrices Cont...
Multiple bands
Vertical
Banding:
Diagonal
Horizontal

4. Types of Sparse Matrices Cont...
Blocking:
Corners
Diagonal

5. Bit Map Compression B Z 5 2 4 9 6 1 3 8 R 1 3 5 6 8 Compressed Matrix
Raw Matrix B Z R

6. Address Map Compression
Compressed Matrix
Raw Matrix A
Array Index Z R

7. Dealing with Empty Rows
R must contain place holders into Z.
Values are set to next non empty row. Z R

8. Dealing with Empty Rows
When a value is entered in row r
Values in Z belonging to r +1 and above are shifted right.
Row index in R is also adjusted +1 for rows above r
In practice, R would contain a dummy column at the end so the last row is not special cased. 7 Z 1 R

9. Orthogonal Linked Lists
Data
Down Row Col Right
Nodes used in the structure
Matrix indices.
Right & down pointers.
Each non-zero entry to the left will be represented by the above node structure.
Structure is linked together using the pointer fields

10. 0 1
12 10
5 0
2 0
8 0
6 0
0 6
0 9
0 2
11 0
0 4 5
2 2 2
2 9 4
5 1 9
5 4 6
6 6 1
8 1 3
8 9 8
11 2

11. Adding [6,4] Find correct row Add Links Find correct Column Add links
0 1
12 10
5 0
2 0
8 0
6 0
0 6
0 9
0 2
11 0
0 4
Adding [6,4] 5
2 2 2
2 9
NEW
6 4
Find correct row
Add Links 4
5 1 9
5 4 6
6 6 1
8 1 3
8 9 8
11 2

12. Relative Compression of Sparse Matrix