Integer sorting is a fundamental problem in computer science. This paper studies parallel integer sort both in theory and in practice. In theory, we show tighter bounds for a class of existing practical integer sort algorithms, which provides a solid theoretical foundation for their widespread use in practice and strong performance. In practice, we design a new integer sorting algorithm, DovetailSort, that is theoretically efficient and has good practical performance.

In particular, DovetailSort overcomes a common challenge in existing parallel integer sorting algorithms, which is the difficulty of detecting and taking advantage of duplicate keys. The key insight in DovetailSort is to combine algorithmic ideas from both integer- and comparison-sorting algorithms. In our experiments, DovetailSort achieves competitive or better performance than existing state-of-the-art parallel integer and comparison sorting algorithms on various synthetic and real-world datasets.