The initial analysis is necessary or
DVD Shrink won't let you shrink the DVD at all.
The deep analysis isn't necessary, but it will help DVD Shrink to better allocate space to the parts of the video that are more complex, and the final result will be better.
I suggest you let DVD Shrink perform the deep analysis whenever it wants to, which is always except when the selected content will fit on a 4.7GB DVD without compression.