Compressed Prefix Sums

Published: 01 Jan 2007, Last Modified: 05 Nov 2024SOFSEM (1) 2007EveryoneRevisionsBibTeXCC BY-SA 4.0
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.
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