Vector Model

In vector model, an algorithm is expressed as a sequence of steps, each of them performs an operation on vector of input values, and produces vector result. Work of each step is equal to length of input or output vector, where as the work of the algorithm is sum of work of its steps. The depth of an algorithm is number of vector steps.

Let there are three vectors $A, B, C$, expressed as $A_1, A_2, \dots A_n$, and $B_1, B_2, \dots, B_n$, and $C_1, C_2, \dots, C_n$. It is required to compute: $C_1 = A_1 \times B_1$, ..., $C_n = A_n \times B_n$. The input vectors are $A, B$ and output vector is $C$. There is only one vector step, i.e., $\times$ on the input vectors. Since size of input is $n$, so work is $n$. The depth is number of vector steps, which is $1$, so parallelism is $n/1 = n$.