Browsing by Author "Rojas-Ledesma, Javiel"

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    Optimal Joins Using Compressed Quadtrees
    (2022) Arroyuelo, Diego; Navarro, Gonzalo; Reutter, Juan L.; Rojas-Ledesma, Javiel
    Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality one either needs to build completely new indexes or must populate the database with several instantiations of indexes such as B+-trees. Either way, this means spending an extra amount of storage space that is typically one or two orders of magnitude more than what is required to store the raw data.
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    Optimizing RPQs over a compact graph representation
    (2024) Arroyuelo, Diego; Gomez-Brandon, Adrian; Hogan, Aidan; Navarro, Gonzalo; Rojas-Ledesma, Javiel
    We propose techniques to evaluate regular path queries (RPQs) over labeled graphs (e.g., RDF). We apply a bit-parallel simulation of a Glushkov automaton representing the query over a ring: a compact wavelet-tree-based index of the graph. To the best of our knowledge, our approach is the first to evaluate RPQs over a compact representation of such graphs, where we show the key advantages of using Glushkov automata in this setting. Our scheme obtains optimal time, in terms of alternation complexity, for traversing the product graph. We further introduce various optimizations, such as the ability to process several automaton states and graph nodes/labels simultaneously, and to estimate relevant selectivities. Experiments show that our approach uses 3-5x\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\times $$\end{document} less space, and is over 5x\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\times $$\end{document} faster, on average, than the next best state-of-the-art system for evaluating RPQs.
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    The Ring: Worst-case Optimal Joins in Graph Databases using (Almost) No Extra Space
    (2024) Arroyuelo Billiardi, Diego Gastón; Gómez-Brandón, Adrián; Hogan, Aidan; Navarro, Gonzalo; Reutter de la Maza, Juan; Rojas-Ledesma, Javiel; Soto, Adrián
    We present an indexing scheme for triple-based graphs that supports join queries in worst-case optimal (wco) time within compact space. This scheme, called a ring, regards each triple as a cyclic string of length 3. Each rotation of the triples is lexicographically sorted and the values of the last attribute are stored as a column, so we obtain the order of the next column by stably re-sorting the triples by its attribute. We show that, by representing the columns with a compact data structure called a wavelet tree, this ordering enables forward and backward navigation between columns without needing pointers. These wavelet trees further support wco join algorithms and cardinality estimations for query planning. While traditional data structures such as B-Trees, tries, and so on, require 6 index orders to support all possible wco joins over triples, we can use one ring to index them all. This ring replaces the graph and uses only sublinear extra space, thus supporting wco joins in almost no space beyond storing the graph itself. Experiments querying a large graph (Wikidata) in memory show that the ring offers nearly the best overall query times while using only a small fraction of the space required by several state-of-the-art approaches. We then turn our attention to some theoretical results for indexing tables of arity d higher than 3 in such a way that supports wco joins. While a single ring of length d no longer suffices to cover all d! orders, we need much fewer rings to index them all: O(2d) rings with a small constant. For example, we need 5 rings instead of 120 orders for d=5. We show that our rings become a particular case of what we dub order graphs, whose nodes are attribute orders and where stably sorting by some attribute leads us from an order to another, thereby inducing an edge labeled by the attribute. The index is then the set of columns associated with the edges, and a set of rings is just one possible graph shape. We show that other shapes, like for example a single ring instead of several ones of length d, can lead us to even smaller indexes, and that other more general shapes are also possible. For example, we handle d=5 attributes within space equivalent to 4 rings.