Housekeeping operations in filters
First, maybe you could give us more context (is that homework?).

I think that what is meant by "housekeeping operations" are the data transfers between registers / state variables ("delay propagation") that naturally arise when naively implementing filters. For example, a naive implementation of a 4-tap FIR would look like this:

output = h[0] * input + h[1] * x[0] + h[2] * x[1] + h[3] * x[2]
// "Housekeeping" operations
x[2] = x[1]
x[1] = x[0]
x[0] = input


The data transfers operations can be avoided on some hardware architectures (especially DSP) by using modulo addressing. I think this is what is meant by "suitable addressing strategies".