Choose an Offset for Compressing Clustered Integers with Outliers

Most integers in a dataset are concentrated in a narrow range, with a few outliers. Choose an offset that reduces storage, and explain how a sliding window can identify a useful range. ### Clarifying Questions The compact bit width, outlier encoding, signedness, metadata cost, and exact storage objective are unspecified. For the worked analysis, choose a fixed w-bit unsigned offset code with a separate inlier/outlier indicator, and store outliers in a wider representation. The offset is stored once per block. These are explicit codec assumptions, not supplied requirements. ### What a Strong Answer Covers A reversible encoding, the range covered by an offset, a maximum-coverage window algorithm, complete storage accounting, and the difference between selecting an offset for fixed width and optimizing the width itself. ### Follow-up Questions - What changes if one compact code value is reserved as an escape marker? - When could offset metadata make compression larger than the original data?