Hinted Dictionaries: Efficient Functional Ordered Sets and Maps

Abstract: This article introduces hinted dictionaries for expressing efficient ordered sets and maps functionally. As opposed to the traditional ordered dictionaries with logarithmic operations, hinted dictionaries can achieve better performance by using cursor-like objects referred to as hints. Hinted dictionaries unify the interfaces of imperative ordered dictionaries (e.g., C++ maps) and functional ones (e.g., Adams' sets). We show that such dictionaries can use sorted arrays, unbalanced trees, and balanced trees as their underlying representations. Throughout the article, we use Scala to present the different components of hinted dictionaries. We also provide a C++ implementation to evaluate the effectiveness of hinted dictionaries. Hinted dictionaries provide superior performance for set-set operations in comparison with the standard library of C++. Also, they show a competitive performance in comparison with the SciPy library for sparse vector operations.