Gilberto Gutiérrez

A spatio-temporal access method based on snapshots and events

This paper describes a new spatio-temporal access method (SEST-Index) that combines two approaches for modeling spatio-temporal information: snapshots and events. This method makes it possible to not only process time slice and interval queries, but also queries about events. The SEST Index implementation uses an R-tree structure for storing snapshots and a log data structure for storing events that occur between consecutive snapshots. Experimental results that compare SEST-Index and HR-tree show that, for a change frequency between 1% and 13%, SEST-Index requires less storage space than HR-tree, and for a change frequency between 1% and 7%, SEST-Index outperforms HR-tree for interval queries. In addition, as SEST-Index is an event-oriented structure, event queries are efficiently answered. In order to decrease the storage space for frequencies of change above 20%, this work explores alternatives that optimize the space of the log structure without affecting the efficiency of query answers.

Finding the largest empty rectangle containing only a query point in large multidimensional databases

Given a two-dimensional space, let S be a set of points stored in an R-tree, let R be the minimum rectangle containing the elements of S, and let q be a query point such that q∉S and R∩q≠∅. In this paper, we present an algorithm for finding the empty rectangle with the largest area, sides parallel to the axes of the space, and containing only the query point q. The idea behind algorithm is to use the points that define the minimum bounding rectangles (MBRs) of some internal nodes of the R-tree to avoid reading as many nodes of the R-tree as possible, given that a naive algorithm must access all of them. We present several experiments considering synthetic and real data. The results show that our algorithm uses around 0.71---38% of the time and around 3---4% of the main storage needed by previous computational geometry algorithms. Furthermore, to the best of our knowledge, this is the first work that solves this problem considering that the points are stored in an R-tree.

The largest empty rectangle containing only a query object in Spatial Databases

Let S be a set of n points in a fixed axis-parallel rectangle

Improved Queryable Representations of Rasters

R\subseteq \Re^{2}

Closest Pair Query on Spatial Data Sets without Index

, i.e. in the two-dimensional space (2D). Assuming that those points are stored in an R-tree, this paper presents several algorithms for finding the empty rectangle in R with the largest area, sides parallel to the axes of the space, and containing only a query point q. This point can not be part of S, that is, it is not stored in the R-tree. All algorithms follow the basic idea of discarding part of the points of S, in such a way that the problem can be solved only considering the remaining points. As a consequence, the algorithms only have to access a very small portion of the nodes (disk blocks) of the R-tree, saving main memory resources and computation time. We provide formal proofs of the correctness of our algorithms and, in order to evaluate the performance of the algorithms, we run an extensive set of experiments using synthetic and real data. The results have demonstrated the efficiency and scalability of our algorithms for different dataset configurations.

Set operations over compressed binary relations

We present two compact representations of rasters, which are used in GIS to represent temperatures, elevations, and other spatial attributes, that support queries on the positions and/or the values stored. These representations are based on space-filling curves and recent advances on compact data structures. They are practical, competitive with recent works on the problem, and present some improved characteristics, such as a nice generalization to time series of rasters, i.e. the storage of several rasters covering the same area at different times.

Linear separability in spatial databases

In this work, we present an algorithm that finds the closest pair on two data sets, assuming that neither set has an index. A straightforward solution is to build the spatial index on the fly, and then apply algorithms that use such indexes. But if the sets are not used again these techniques are inefficient. Our algorithm considers two steps: First, each set is partitioned into a collection of subsets, or clusters, spatially defined by means of an MBR (Minimum Bounding Rectangle). The second step consists in processing the partitions using a family of metrics defined for the MBRs, as a filter for finding the closest pair. We experimentally compared our proposal with techniques that use indexes and techniques that do not. The results of our experiments shown that our algorithm overcome these techniques on several realist scenarios.

The largest empty circle with location constraints in spatial databases

Abstract Binary relations are commonly used to represent relationships between real-world objects. Classical representations for binary relations can be very space-consuming when the set of elements is large. In these cases, compressed representations, such as the k 2 -tree, have proven to be a competitive solution, as they are efficient in time while consuming very little space. Moreover, k 2 -trees can successfully represent both sparse and dense binary relations, using different variants of the technique. In this paper, we propose and evaluate algorithms to efficiently perform set operations over binary relations represented using k 2 -trees. More specifically, we present algorithms for computing the union, intersection, difference, symmetric difference, and complement of binary relations. Thus, this work extends the functionality of the different variants of the k 2 -tree representation for binary relations. Our algorithms are computed directly over the compressed representation, without requiring previous decompression, and generate the result in compressed form. The experimental evaluation shows that they are efficient in terms of space and time, compared with different baselines where the binary relations are represented in plain form or require a previous decompression to perform the set operation.

A Genetic Algorithm for the Generation of Packetization Masks for Robust Image Communication

Given two spatial point sets R and B in the plane, with cardinalities m and n, respectively, and stored in two separate R-trees, we propose an efficient algorithm to verify whether R and B are linearly separable. The sets R and B are linearly separable if there exists a line that splits the plane into to halfplanes, one containing all R and the other one containing all B. This is the first algorithm that answers the separability question in the context of the spatial data bases. That is, it considers as input big spatial data stored in secondary storage data structures (e.g., the R-tree) which are not allowed to be completely stored in the main memory of the computer to run a classic algorithm. The algorithms designed in this context aim to minimize as much as possible the number of blocks read from the secondary storage data structures to the main memory. Studied problems in this setting are the k-nearest neighbor problem and the spatial range query problem. Our algorithm explicitly exploits the geometric and spatial properties of the R-trees to access only the nodes relevant to decide the linear separability of the given sets. Our experimental results show the efficiency of the algorithm, since it accesses between the 0.34 and 2.79% of the nodes of the R-trees. We also analyze the asymptotic running time of the algorithm, showing that it runs in