Sorttia

Sorttia is a theoretical, cache-conscious sorting technique described in discussions of modern sorting algorithms. It partitions the input sequence into contiguous blocks, or tiles, sized to fit within a target level of the memory hierarchy. Each block is sorted independently, using a method appropriate for its size; small blocks often employ insertion sort, while larger blocks use a conventional comparison-based sort.

After the in-block sorting, the algorithm performs a multi-way merge of the sorted blocks, producing a globally ordered sequence. The merge is designed to preserve stability, ensuring equal elements retain their relative order from the input.

The design goal of Sorttia is to maximize data locality and reduce cache misses, thereby improving real-world performance on contemporary hardware. Block size and merge strategy may be tuned to exploit specific cache sizes, vector units, or memory bandwidth. Some implementations use in-place merging to limit extra space, at the cost of added complexity, while others rely on a dedicated auxiliary buffer.

Complexity characteristics align with typical comparison-based sorts: average-case time on the order of O(n log n) with practical performance governed by cache behavior. Space usage varies with the merge approach, ranging from O(n) auxiliary space to in-place variants with additional overhead.

Sorttia is mainly discussed in theoretical and pedagogical contexts as a model for understanding cache-aware sorting strategies. It shares ideas with tile-based and block-based sorts, and is related to, but distinct from, algorithms such as merge sort, quicksort variants, and Timsort. See also: Merge sort, Timsort, cache-oblivious sorting.