Need for Speed Sort: A Recursive Distribution-Based Sorting Algorithm

Abstract

We present Need for Speed Sort (NFS Sort), a recursive distribution-based sorting algorithm designed for numeric arrays. The algorithm partitions elements into equal-width value intervals, recursively refines dense buckets, and propagates analytical interval bounds between recursive calls, avoiding repeated scans for local minima and maxima. NFS Sort combines a fragment-based, cache-conscious scatter procedure for large subarrays with a lower-overhead auxiliary-array approach for smaller inputs. Small buckets are deferred to a final insertion-sort cleanup, while a comparison-based fallback is activated when recursive partitioning repeatedly fails to reduce the problem size. This mechanism guarantees a worst-case running time of O(n log n) and auxiliary space usage of O(log n). Experimental evaluation on synthetic inputs and real-world datasets from the SOSD benchmark suite compares NFS Sort with Balanced Learned Sort, IPS4o, Boost Spreadsort, PDQSort, and std::sort. The results show that NFS Sort is competitive or better than established state-of-the-art sorting methods across dataset sizes and distributions, outperforming the learned baseline particularly on smaller inputs while retaining strong performance at larger scales. Overall, NFS Sort combines efficient recursive distribution, practical memory management, and robust worst-case guarantees for high-performance numeric sorting.