two parts:
1, task represented by DAG
edges << operations => better for parallelism
2, programming model defining DAG
work span analysis
https://maths-people.anu.edu.au/~brent/pub/pub022.html
second condition
brent's theorem:
https://crd-legacy.lbl.gov/~dhbailey/dhbpapers/twelve-ways.pdf
The correct answer depends on the situation.
The Holy Grail for span is to find a poly-logarithmic algorithm
replace par-for with a procedure call
for i loop, the y[i]s are independent from each other
but for j loop, every component depends on y[i]
eg
j loop is linear and executed by n times.
t[:] ← A[i,:] cdot x[:]
linear work and logarithmic span (look at the forth slide of this page)
https://www.cprogramming.com/parallelism.html
