Joins via Geometric Resolutions: Worst Case and Beyond

• Autores: Mahmoud Abo Khamis, Hung Q. Ngo, Christopher Ré, Atri Rudra
• Localización: ACM transactions on database systems, ISSN 0362-5915, Vol. 41, Nº 4 (Invited Paper from EDBT 2015, Invited Paper from PODS 2015 and Regular Papers), 2016
• Idioma: inglés
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• Resumen

  • 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.