Efficient indexing is fundamental to managing and analyzing multi-dimensional data. A growing trend is to directly learn the storage layout of multi-dimensional data using simple machine learning models, leading to the concept of Learned Index . Compared to conventional indexing methods that have been used for decades (e.g., k d-tree and R-tree variants), learned indexes have demonstrated empirical advantages in both space and time efficiency on modern architectures. However, there is a lack of comprehensive evaluation across existing multi-dimensional learned indexes under a standardized benchmark, making it challenging to identify the most suitable index for specific data types and query patterns. This gap also hinders the widespread adoption of learned indexes in practical applications. In this paper, we present the first in-depth empirical study to answer the question: how good are multi-dimensional learned indexes? We evaluate ten recently published indexes under a unified experimental framework, which includes standardized implementations, datasets, query workloads, and evaluation metrics. We thoroughly investigate the evaluation results and discuss the findings that may provide insights for future learned index design.

In this paper, we study the privacy-preserving task assignment problem in spatial crowdsourcing, where the locations of both workers and tasks, prior to their release to the server, are perturbed with Geo-Indistinguishability (a differential privacy notion for location-based systems). Different from the previously studied online setting, where each task is assigned immediately upon arrival, we target the batch-based setting, where the server maximizes the number of successfully assigned tasks after a batch of tasks arrive. To achieve this goal, we propose the k-Switch solution, which first divides the workers into small groups based on the perturbed distance between workers/tasks, and then utilizes Homomorphic Encryption (HE) based secure computation to enhance the task assignment. Furthermore, we expedite HE-based computation by limiting the size of the small groups under k. Extensive experiments demonstrate that, in terms of the number of successfully assigned tasks, the k-Switch solution improves batch-based baselines by 5.9X and the existing online solution by 1.74X, with no privacy leak.