Joins via Geometric Resolutions: Worst-case and Beyond · HackerPapers discussions

Joins via Geometric Resolutions: Worst-case and Beyond — mentioned by namibj

Sat, 30 Jul 2022 05:56:01 GMT

Funnily enough, this hypergraph view is used to describe symptomatic query complexity for cyclical joins, the simplest if which is "count triangles in adjacency list" (naive RDBMS yields O(n²) on pathological data, despite the wrist case optimal tactic being something like O(n + #Triangles), with #Triangles limited inherently to O(n^(1.5))). See https://arxiv.org/abs/1404.0703 for some reading material and one particular way at beyond worst case (i.e., sharing worst case asympotics with the best constant time algorithm, but better performance on non-pathological data (a more precise notion is…

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Joins via Geometric Resolutions: Worst-case and Beyond — mentioned by j-pb

Sun, 03 Jan 2021 10:24:49 GMT

It's all about efficient range reads and seek operations. You can compute set operations pretty efficiently using sorted indices that support a "find next or greater" operation. For intersection, take the first value from the first set as the smallest candidate of the output set, then call call candidate := next(candidate) on each set, updating the candidate with the next smallest possible value, and adding it to the output set when a candidate was returned by all sets. The algorithm is worst case optimal up to a log factor, and can even be extended to perform generic constraint programming…

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Joins via Geometric Resolutions: Worst-case and Beyond — mentioned by j-pb

Mon, 09 Dec 2019 14:09:04 GMT

Out of the examples I would take a look at the LogicBlox Stuff, they gave join algorithm research a big push with their Leapfrog-Triejoin. The following papers ascend in difficulty, and are based on each other, but offer a fascinating glimpse into the connection of DPLL SAT solving and Conjunctive Query evaluation. https://openproceedings.org/2014/conf/icdt/Veldhuizen14.pdf https://arxiv.org/abs/1310.3314 https://arxiv.org/abs/1404.0703 As for reasoning and decidability, I think we need to clarify the decidability we're talking about. Decision problems are decidable or undecidable, and when…

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Joins via Geometric Resolutions: Worst-case and Beyond — mentioned by jamii

Fri, 09 Oct 2015 08:54:34 GMT

Frustratingly light on detail, but the possible connections to http://arxiv.org/abs/1404.0703 are intriguing.

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Joins via Geometric Resolutions: Worst-case and Beyond — mentioned by jamii

Sat, 24 Jan 2015 00:32:28 GMT

Some of the more exciting ideas I've seen recently: http://arxiv.org/abs/1310.3314 - Understanding the core difficulty in answering relational queries and examples of problems for which current query optimisers always produce plans which are asymptotically suboptimal http://arxiv.org/abs/1404.0703 - The first theoretical analysis which can relate the choice of indexes to worst-case bounds. Presents a single join algorithm which is asymptotically optimal on every problem without even using cardinality estimates. http://arxiv.org/abs/1210.0481 - A join algorithm that meets some of the bounds of…

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