Title: Index2Sort: Sorting Algorithm Using Static Index Data Structure
Primary area: learning theory
Keywords: sorting algorithm, index data structure, algorithms with predictions, learned sort, learned index

Abstract: We introduce Index2Sort, a general framework for deriving sorting algorithms from static indexes.
Index2Sort treats the index as an opaque box that exposes only two operations: index construction and rank queries.
This abstraction allows Index2Sort to be applied to various index structures, including classical and learned indexes.
Our theoretical analysis shows that the computational guarantees of the index transfer directly to Index2Sort.
If the index can be constructed in expected time $\mathcal{O}(nC(n))$ and can answer rank queries in expected time $\mathcal{O}(Q(n))$, then Index2Sort sorts the input in expected time $\mathcal{O}(nC(n) + nQ(n))$.
In particular, when using a state-of-the-art learned index with $C(n)=Q(n)=1$, this yields an expected complexity of $\mathcal{O}(n)$, which is a strictly tighter bound than those of existing learned sorting algorithms.
In contrast to recent theoretical works on learned sorting, which derive complexity guarantees by analyzing the internal structure of a learned index and designing a sorting algorithm with a similar structure, Index2Sort achieves stronger guarantees without requiring any inspection or modification of the index internals.

TL;DR: We propose Index2Sort, a framework that converts any static index into a sorting algorithm, achieving O(n) expected time with modern learned indexes—without inspecting or modifying the index internals.