Optimization of Base-n Radix Sort for Skewed Datasets

2025-09-23

AI Summary

Base-n radix sort (BNRS) suffers from poor efficiency on skewed integer datasets—characterized by numerous small values and a few extremely large ones—due to redundant scans of high-order zero-padded regions and fixed partitioning granularity. Method: This paper proposes a logical partitioning optimization for BNRS. Its core innovation is a stable in-place partitioning mechanism that dynamically reduces the size of subproblems in each radix pass, combined with a logical subgroup partitioning strategy that eliminates unnecessary traversal of leading-zero segments. Contribution/Results: Theoretical analysis shows that when the key parameter (k < n log_2 n), the algorithm achieves asymptotically better time complexity than conventional comparison-based sorting. Experimental evaluation on skewed datasets demonstrates significant speedup—averaging 2.1× over standard BNRS—while preserving in-place space complexity with no additional auxiliary storage.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Optimization
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The importance and applications of sorting is apparent and needs no explanation. In this paper, we analyse a non-comparison sorting algorithm, Base-n Radix Sort (BNRS) and introduce an optimized vari- ant of BNRS, namely, Stable Logical Partition Radix Sort (SLPR). The complexity of these algorithms is measured by the input size $n$ and the maximum value $k$. We show that with respect to time complexity, these algorithms are more succinct than traditional comparison-based sorting algorithms for representing the sorted order of certain integer distribu- tions, specifically, when $k <nlog_2^n$ is met. We also show that the SLPR optimization, which uses in-place stable partitioning to reduce the active problem size in each pass, resulting in highly effective sorting for skewed datasets that contain a majority of small numbers and mix of very large numbers.

Problem

• Optimizing Base-n Radix Sort for skewed datasets
• Improving sorting efficiency for specific integer distributions
• Reducing active problem size using in-place stable partitioning

Innovation

• Optimized Base-n Radix Sort algorithm
• Uses in-place stable partitioning technique
• Reduces active problem size each pass