Evaluating the complexity of an algorithm is an important step when developing applications, as it impacts both its time and energy performance. Computational complexity, which is the number of dynamic operations regardless of the execution order, is easy to characterize for affine programs. Data movement (or, I/O) complexity is more complex to evaluate as it refers, when considering all possible valid schedules, to the minimum required number of I/O between a slow (e.g. main memory) and a fast (e.g. local scratchpad) storage location.

Researchers and practitioners have for long worked on improving the computational complexity of algorithms, focusing on reducing the number of operations needed to perform a computation. However the hardware trend nowadays clearly shows a higher performance and energy cost for data movements than computations: quality algorithms have to minimize data movements as much as possible.