Onion Curve: A Space Filling Curve with Near-Optimal Clustering

Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the {\em onion curve}, an SFC whose clustering performance is provably close to optimal for the cube and near-cube shaped query sets, irrespective of the side length of the query. We show that in contrast, the clustering performance of the widely used Hilbert curve can be far from optimal, even for cube-shaped queries. Since the clustering performance of an SFC is critical to the efficiency of multi-dimensional indexes based on the SFC, the onion curve can deliver improved performance for data structures involving multi-dimensional data.Comment: The short version is published in ICDE 1

SFour: A Protocol for Cryptographically Secure Record Linkage at Scale

The prevalence of various (and increasingly large) datasets presents the challenging problem of discovering common entities dispersed across disparate datasets. Solutions to the private record linkage problem (PRL) aim to enable such explorations of datasets in a secure manner. A two-party PRL protocol allows two parties to determine for which entities they each possess a record (either an exact matching record or a fuzzy matching record) in their respective datasets — without revealing to one another information about any entities for which they do not both possess records. Although several solutions have been proposed to solve the PRL problem, no current solution offers a fully cryptographic security guarantee while maintaining both high accuracy of output and subquadratic runtime efficiency. To this end, we propose the first known efficient PRL protocol that runs in subquadratic time, provides high accuracy, and guarantees cryptographic security