You may assume that the actual running time of a parallel program on a dedicated P -processor machine is

 

Your research group has produced two chess programs, a simple one and an optimized one. The simple one has T1 = 2048 seconds and T∞ = 1 second. Whenyou run it on your 32-processor machine, sure enough, the running time is 65 steps. Your students then produce an “optimized” version with T 1 = 1024 seconds and T∞ = 8 seconds. Why is it optimized? When you run it on your 32-processor machine, the running time is 40 steps, as predicted by our formula. Which program will scale better to a 512-processor machine?

Tp=T/P+Too-