Leveraging Soft Functional Dependencies for Indexing Multi-dimensional Data

A new proposal in database indexing has been for index structures to automatically learn and use the distribution of the underlying data to improve their performance. Initial work on \textit{learned indexes} has repeatedly shown that by learning the distribution of the data, index structures such as the B-Tree, can boost their performance by an order of magnitude while using a smaller memory footprint. In this work we propose a new class of learned indexes for multidimensional data that instead of learning only from distribution of keys, learns from correlations between columns of the dataset. Our approach is motivated by the observation that in real datasets, correlation between two or more attributes of the data is a common occurrence. This idea of learning from functional dependencies has been previously explored and implemented in many state of the art query optimisers to predict selectivity of queries and come up with better query plans. In this project we aim to take the use of learned functional dependencies a step further in databases. Consequently, we focus on using learned functional dependencies to reduce the dimensionality of datasets. With this we attempt to work around the curse of dimensionality - which in the context of spatial data stipulates that with every additional dimension, the performance of an index deteriorates further - to accelerate query execution. In more precise terms, we learn how to infer one (or multiple) attributes from the remaining attributes and hence no longer need to index predicted columns. This method reduces the dimensionality of the index and thus makes it more efficient. We show experimentally that by predicting correlated attributes in the data, rather than indexing them, we can improve the query execution time and reduce the memory overhead of the index at the same time.