14. !14
GrB assign (v, q, NULL, level, GrB ALL, n, NULL)
v <q> = level ; // assig
v: q:
. .
. .
. .
1 1
. .
. .
. .
gn (v, q, NULL, level, GrB ALL, n, NULL)
v <q> = level ; // assign level
v: q:
. .
. .
. .
1 1
. .
. .
. .
15. !15
GrB mxv (q, v, NULL, GxB LOR LAND BOOL, A, q, desc)
first part of q<!>=A*q:
t = A*q ;
xv (q, v, NULL, GxB LOR LAND BOOL, A, q, desc)
first part of q<!>=A*q:
t = A*q ;
16. !16
GrB mxv (q, v, NULL, GxB LOR LAND BOOL, A, q, desc)
second part of q<!>=A*q:
q = false (n,1) ;
q <!v> = t ;
v: t=A*q: q<!v>=t
. 1 1
. . .
. 1 1
1 . .
. . .
. . .
. . .
v (q, v, NULL, GxB LOR LAND BOOL, A, q, desc)
second part of q<!>=A*q:
q = false (n,1) ;
q <!v> = t ;
v: t=A*q: q<!v>=t
. 1 1
. . .
. 1 1
1 . .
. . .
. . .
. . .
17. gn (v, q, NULL, level, GrB ALL, n, NULL)
v <q> = level ; // assign level
v: q:
2 1
. .
2 1
1 .
. .
. .
. .
GrB assign (v, q, NULL, level, GrB ALL, n, NULL)
v <q> = level ; // a
v: q:
2 1
. .
2 1
1 .
. .
. .
. .
18. GrB mxv (q, v, NULL, GxB LOR LAND BOOL, A, q, desc
first part of q<!>=A*q:
t = A*q ;
q, v, NULL, GxB LOR LAND BOOL, A, q, desc)
first part of q<!>=A*q:
t = A*q ;
19. Binary matrix
1 bit per matrix cell
1,000,000 X 1,000,000
One 10^12 (trillion) bits = 125GB
……………………………………………………….
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……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
……………………………………………………….
!19
20. Real world graphs
Most real world graphs are sparse
Facebook
2 billion users
338 friends for user on average
2,000,000,000 * 338 / 2,000,000,000^2
0.000000169% utilisation
!20