1. Parallel Speedup

2. Performance of a Parallel Algorithm
n : problem size (e.g.: sort n numbers)
p : number of processors
Tp : parallel time
Ts : sequential time (optimal sequ. alg.)
S = Ts / Tp : speedup (1Sp) S
S=p
super-linear
linear
sub-linear p

3. Speedup linear speedup S = p optimal
super linear speedup S > p : impossible
Proof. Assume that parallel algorithm A has a speedup S > p for processors, i.e. S = Ts / Tp > p. Hence: Ts > T·p. Simulate A on a sequential, single processor machine. Then Tp(1) = Tp · p < Ts. Hence, Ts was not optimal. Contradiction.

4. S p

5. Scaled Speedup
Ts may be unknown (in fact, for most real experiments this is the case)
Scaled speedup S’ = Tp(1) / Tp(p)
S’  S

6. Efficiency e = S / p efficiency (0e1)
optimal linear speedup S = p  e = 1
e’ = S’ / p scaled efficiency