Virtual-Memory Powersort

2026-05-26

AI Summary

This work addresses the high memory overhead of adaptive merge sort algorithms in stable sorting, which typically require O(n) auxiliary buffer space. We propose Virtual-Memory Powersort, an almost-in-place stable sorting algorithm based on internal buffering techniques that reduces the extra space complexity to O(√(n log n)). By integrating Powersort’s optimal merging strategy, our method effectively minimizes both data movement and comparison costs. Experimental results demonstrate that Virtual-Memory Powersort achieves runtime performance comparable to state-of-the-art stable sorting algorithms while substantially lowering memory consumption, thereby offering an efficient and memory-frugal solution for stable sorting.

Abstract

We give a more space-efficient implementation of adaptive mergesort: Virtual-Memory Powersort. Using internal buffering techniques, we significantly reduce the memory consumption of the algorithm; specifically, for sorting $n$ objects the required buffer area is reduced from space for $n/2$ objects to $O(\sqrt{n \log n})$ objects. While this space-efficiency can be achieved (indeed reduced to $O(1)$) conceptually very easily with known inplace merging algorithms, using these as a drop-in replacement for the standard merge algorithm incurs a substantial slow-down. Virtual-Memory Powersort, by contrast, uses the same number of moves and comparisons as previous Powersort implementations up to an additive $O(n)$ term. We report on an empirical running-time study comparing our implementation against other Powersort variants and state-of-the-art stable sorting methods, demonstrating that almost in-place stable sorting can be achieved with negligible overhead in many scenarios.

Problem

• stable sorting
• space efficiency
• adaptive mergesort
• in-place sorting
• memory consumption

Innovation

• Virtual-Memory Powersort
• adaptive mergesort
• internal buffering
• space-efficient sorting
• stable sorting