arXiv subjects

Javiel Rojas-Ledesma

Publications and source records attributed to Javiel Rojas-Ledesma.

5 recordsLinked to original sources

arXiv2021

Time- and Space-Efficient Regular Path Queries on Graphs

We introduce a time- and space-efficient technique to solve regularpath queries over labeled graphs. We combine a bit-parallel simula-tion of the Glushkov automaton of the regular expression with thering index introduced by Arroyuelo et al., exploiting its wavelettree representation of the triples in order to efficiently reach thestates of the product graph that are relevant for the query. Ourquery algorithm is able to simultaneously process several automa-ton states, as well as several graph nodes/labels. Our experimentalresults show that our representation uses 3-5 times less space thanthe alternatives in the literature, while generally outperformingthem in query times (1.67 times faster than the next best).

cs.DB↗

arXiv2020

Optimal Joins using Compact Data Structures

Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with 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 we either need to build completely new indexes, or we 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 may be non-negligible. We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quad tree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal.

cs.DB↗

arXiv2018

Computing Coverage Kernels Under Restricted Settings

We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems on graphs, the problem becomes solvable in polynomial time under restrictions on the graph induced by $B$. We consider various classes of graphs, show that Minimum Coverage Kernel remains $\mathsf{NP}$-hard even for severely restricted instances, and provide two polynomial time approximation algorithms for this problem.

cs.CG↗

arXiv2017

Depth Distribution in High Dimensions

Motivated by the analysis of range queries in databases, we introduce the computation of the Depth Distribution of a set $\mathcal{B}$ of axis aligned boxes, whose computation generalizes that of the Klee's Measure and of the Maximum Depth. In the worst case over instances of fixed input size $n$, we describe an algorithm of complexity within $O({n^\frac{d+1}{2}\log n})$, using space within $O({n\log n})$, mixing two techniques previously used to compute the Klee's Measure. We refine this result and previous results on the Klee's Measure and the Maximum Depth for various measures of difficulty of the input, such as the profile of the input and the degeneracy of the intersection graph formed by the boxes.

cs.CG↗

arXiv2015

Adaptive Computation of the Klee's Measure in High Dimensions

The KLEE'S MESURE of $n$ axis-parallel boxes in $\mathbb{R}^d$ is the volume of their union. It can be computed in time within $O(n^{d/2})$ in the worst case. We describe three techniques to boost its computation: one based on some type of "degeneracy'' of the input, and two ones on the inherent "easiness'' of the structure of the input. The first technique benefits from instances where the MAXIMA of the input is of small size $h$, and yields a solution running in time within $O(n\log^{2d-2}{h}+ h^{d/2}) \subseteq O(n^{d/2}$). The second technique takes advantage of instances where no $d$-dimensional axis-aligned hyperplane intersects more than $k$ boxes in some dimension, and yields a solution running in time within $O(n \log n + n k^{(d-2)/2}) \subseteq O(n^{d/2})$. The third technique takes advantage of instances where the \emph{intersection graph} of the input has small treewidth $ω$. It yields an algorithm running in time within $O(n^4ω\log ω+ n (ω\log ω)^{d/2})$ in general, and in time within $O(n \log n + n ω^{d/2})$ if an optimal tree decomposition of the intersection graph is given. We show how to combine these techniques in an algorithm which takes advantage of all three configurations.

cs.DS↗