Browsing by Author "Gómez-Brandón, Adrián"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Worst-Case-Optimal Similarity Joins on Graph Databases
    (2024) Arroyuelo Billiardi, Diego Gastón; Bustos, Benjamin; Gómez-Brandón, Adrián; Hogan, Aidan; Navarro, Gonzalo; Reutter de la Maza, Juan
    We extend the concept of worst-case optimal equijoins in graph databases to the case where some nodes are required to be within the k-nearest neighbors (kNN) of others under some similarity function. We model the problem by superimposing the database graph with the kNN graph and show that a variant of Leapfrog TrieJoin (LTJ) implemented over a compact data structure called the Ring can be seamlessly extended to integrate similarity clauses with the equijoins in the LTJ query process, retaining worst-case optimality in many relevant cases. Our experiments on a benchmark that combines Wikidata and IMGpedia show that our enhanced LTJ algorithm outperforms by a considerable margin a baseline that first applies classic LTJ and then completes the query by applying the similarity predicates. The difference is more pronounced on queries where the similarity clauses are more densely connected to the query, becoming of an order of magnitude in some cases.