Compressed Representations of Conjunctive Query Results

Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a data processing pipeline. Motivated by this problem, we study the construction of space-efficient compressed representations of the output of conjunctive queries, with the goal of supporting the efficient access of the intermediate compressed result for a given access pattern. In particular, we initiate the study of an important tradeoff: minimizing the space necessary to store the compressed result, versus minimizing the answer time and delay for an access request over the result. Our main contribution is a novel parameterized data structure, which can be tuned to trade off space for answer time. The tradeoff allows us to control the space requirement of the data structure precisely, and depends both on the structure of the query and the access pattern. We show how we can use the data structure in conjunction with query decomposition techniques, in order to efficiently represent the outputs for several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom

Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles

In this paper we study two geometric data structure problems in the special case when input objects or queries are fat rectangles. We show that in this case a significant improvement compared to the general case can be achieved. We describe data structures that answer two- and three-dimensional orthogonal range reporting queries in the case when the query range is a \emph{fat} rectangle. Our two-dimensional data structure uses $O(n)$ words and supports queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the data structure, $U$ is the size of the universe and $k$ is the number of points in the query range. Our three-dimensional data structure needs $O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U + k)$ time. We also consider the rectangle stabbing problem on a set of three-dimensional fat rectangles. Our data structure uses $O(n)$ space and answers stabbing queries in $O(\log U\log\log U +k)$ time.Comment: extended version of a WADS'19 pape

FRESH: Fréchet similarity with hashing

This paper studies the r-range search problem for curves under the continuous Fréchet distance: given a dataset S of n polygonal curves and a threshold >0 , construct a data structure that, for any query curve q, efficiently returns all entries in S with distance at most r from q. We propose FRESH, an approximate and randomized approach for r-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. We experimentally compare FRESH to exact and deterministic solutions, and we show that high performance can be reached by suitably relaxing precision and recall

Optimal deterministic shallow cuttings for 3D dominance ranges

Shallow cuttings are one of the most fundamental tools in range searching as many problems in the field admit efficient static data structures due to their application. We present the first efficient deterministic algorithms that given a set of n three-dimensional points, they construct optimal size (single and multiple) shallow cuttings for orthogonal dominance ranges. In particular, we show how to construct a single shallow cutting in O(n log n) worst case time, using O(n) space. We also show how to construct in the same complexity, a logarithmic number of shallow cuttings of the input simultaneously. Our algorithms are optimal in the comparison and the algebraic comparison models, and they are an important step forward, since only polynomial guarantees were previously achieved for the deterministic construction of shallow cuttings, even in three dimensions. In fact, our methods yield the first worst case efficient preprocessing algorithms for a series of important orthogonal range searching problems in the pointer machine and the word-RAM models, where such shallow cuttings are utilised to support the queries efficiently. Copyright © 2014 by the Society for Industrial and Applied Mathematics

On the Spectrum of the Forced Matching Number of Graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M , such that S is contained in no other perfect matching of G. This notion originally arose in chemistry in the study of molecular resonance structures. Similar concepts have been studied for block designs and graph colorings under the name de ning set, and for Latin squares under the name critical set. Recently several papers have appeared on the study of forcing sets for other graph theoretic concepts such as dominating sets, orientations, and geodetics. Whilst there has been some study of forcing sets of matchings of hexagonal systems in the context of chemistry, only a few other classes of graphs have been considered