Joins via Geometric Resolutions: Worst-case and Beyond
Abstract
We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as beyond worst-case results. The framework allows us to prove results for data stored in Btrees, multidimensional data structures, and even multiple indices per table. A key idea in our framework is formalizing the inference one does with an index as a type of geometric resolution; transforming the algorithmic problem of computing joins to a geometric problem. Our notion of geometric resolution can be viewed as a geometric analog of logical resolution. In addition to the geometry and logic connections, our algorithm can also be thought of as backtracking search with memoization.
Cite
@article{arxiv.1404.0703,
title = {Joins via Geometric Resolutions: Worst-case and Beyond},
author = {Mahmoud Abo Khamis and Hung Q. Ngo and Christopher Ré and Atri Rudra},
journal= {arXiv preprint arXiv:1404.0703},
year = {2016}
}