Compressed Prefix Sums

O'Neil Delpratt, Naila Rahman, Rajeev Raman

Abstract: We consider the prefix sums problem: given a (static) sequence of positive integers \(\vec{x} = (x_1, \ldots, x_n)\), such that \(\sum_{i=1}^n x_i = m\), we wish to support the operation \({\sf sum}(\vec{x},j)\), which returns \(\sum_{i=1}^{j} x_i\). Our interest is in minimising the space required for storing \(\vec{x}\), where ‘minimal space’ is defined according to some compressibility criteria, while supporting sum as rapidly as possible.