Parallel In-Memory Evaluation of Spatial Joins

The spatial join is a popular operation in spatial database systems and its evaluation is a well-studied problem. As main memories become bigger and faster and commodity hardware supports parallel processing, there is a need to revamp classic join algorithms which have been designed for I/O-bound processing. In view of this, we study the in-memory and parallel evaluation of spatial joins, by re-designing a classic partitioning-based algorithm to consider alternative approaches for space partitioning. Our study shows that, compared to a straightforward implementation of the algorithm, our tuning can improve performance significantly. We also show how to select appropriate partitioning parameters based on data statistics, in order to tune the algorithm for the given join inputs. Our parallel implementation scales gracefully with the number of threads reducing the cost of the join to at most one second even for join inputs with tens of millions of rectangles.Comment: Extended version of the SIGSPATIAL'19 paper under the same titl

Enhancing In-Memory Spatial Indexing with Learned Search

Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enableddevices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and social media platforms (e.g.,location-tagged posts on Facebook, Twitter, and Instagram). This exponential growth in spatial data has led the research communityto build systems and applications for efficient spatial data processing.In this study, we apply a recently developed machine-learned search technique for single-dimensional sorted data to spatial indexing.Specifically, we partition spatial data using six traditional spatial partitioning techniques and employ machine-learned search withineach partition to support point, range, distance, and spatial join queries. Adhering to the latest research trends, we tune the partitioningtechniques to be instance-optimized. By tuning each partitioning technique for optimal performance, we demonstrate that: (i) grid-basedindex structures outperform tree-based index structures (from 1.23× to 2.47×), (ii) learning-enhanced variants of commonly used spatialindex structures outperform their original counterparts (from 1.44× to 53.34× faster), (iii) machine-learned search within a partitionis faster than binary search by 11.79% - 39.51% when filtering on one dimension, (iv) the benefit of machine-learned search diminishesin the presence of other compute-intensive operations (e.g. scan costs in higher selectivity queries, Haversine distance computation, andpoint-in-polygon tests), and (v) index lookup is the bottleneck for tree-based structures, which could potentially be reduced by linearizingthe indexed partitions.Additional Key Words and Phrases: spatial data, indexing, machine-learning, spatial queries, geospatia

SwiftSpatial: Spatial Joins on Modern Hardware

Spatial joins are among the most time-consuming queries in spatial data management systems. In this paper, we propose SwiftSpatial, a specialized accelerator architecture tailored for spatial joins. SwiftSpatial contains multiple high-performance join units with innovative hybrid parallelism, several efficient memory management units, and an integrated on-chip join scheduler. We prototype SwiftSpatial on an FPGA and incorporate the R-tree synchronous traversal algorithm as the control flow. Benchmarked against various CPU and GPU-based spatial data processing systems, SwiftSpatial demonstrates a latency reduction of up to 5.36x relative to the best-performing baseline, while requiring 6.16x less power. The remarkable performance and energy efficiency of SwiftSpatial lay a solid foundation for its future integration into spatial data management systems, both in data centers and at the edge

APRIL: Approximating Polygons as Raster Interval Lists

The spatial intersection join an important spatial query operation, due to its popularity and high complexity. The spatial join pipeline takes as input two collections of spatial objects (e.g., polygons). In the filter step, pairs of object MBRs that intersect are identified and passed to the refinement step for verification of the join predicate on the exact object geometries. The bottleneck of spatial join evaluation is in the refinement step. We introduce APRIL, a powerful intermediate step in the pipeline, which is based on raster interval approximations of object geometries. Our technique applies a sequence of interval joins on 'intervalized' object approximations to determine whether the objects intersect or not. Compared to previous work, APRIL approximations are simpler, occupy much less space, and achieve similar pruning effectiveness at a much higher speed. Besides intersection joins between polygons, APRIL can directly be applied and has high effectiveness for polygonal range queries, within joins, and polygon-linestring joins. By applying a lightweight compression technique, APRIL approximations may occupy even less space than object MBRs. Furthermore, APRIL can be customized to apply on partitioned data and on polygons of varying sizes, rasterized at different granularities. Our last contribution is a novel algorithm that computes the APRIL approximation of a polygon without having to rasterize it in full, which is orders of magnitude faster than the computation of other raster approximations. Experiments on real data demonstrate the effectiveness and efficiency of APRIL; compared to the state-of-the-art intermediate filter, APRIL occupies 2x-8x less space, is 3.5x-8.5x more time-efficient, and reduces the end-to-end join cost up to 3 times.Comment: 12 page

The Complexity of Boolean Conjunctive Queries with Intersection Joins

Intersection joins over interval data are relevant in spatial and temporal data settings. A set of intervals join if their intersection is non-empty. In case of point intervals, the intersection join becomes the standard equality join. We establish the complexity of Boolean conjunctive queries with intersection joins by a many-one equivalence to disjunctions of Boolean conjunctive queries with equality joins. The complexity of any query with intersection joins is that of the hardest query with equality joins in the disjunction exhibited by our equivalence. This is captured by a new width measure called the IJ-width. We also introduce a new syntactic notion of acyclicity called iota-acyclicity to characterise the class of Boolean queries with intersection joins that admit linear time computation modulo a poly-logarithmic factor in the data size. Iota-acyclicity is for intersection joins what alpha-acyclicity is for equality joins. It strictly sits between gamma-acyclicity and Berge-acyclicity. The intersection join queries that are not iota-acyclic are at least as hard as the Boolean triangle query with equality joins, which is widely considered not computable in linear time

On the complexity of queries with intersection joins

This thesis studies the complexity of join processing on interval data. It defines a class of queries, called Conjunctive Queries with Intersections Joins (IJQs). An IJQ is a query in which the variables range both over scalars and intervals with real-valued endpoints. The joins are expressed through intersection predicates; an intersection predicate over a multi-set that consists of both scalars and intervals is a true assertion, if the elements in the multi-set intersect; otherwise, it is false. The class of IJQs includes queries that are often asked in practice. This thesis introduces techniques for obtaining reductions from the problem of evaluating IJQs to the problem of evaluating Conjunctive Queries with Equality Joins (CQs). The key idea is the rewriting of an intersection predicate over a set of intervals into an equivalent predicate with equality conditions. This rewriting is achieved by building a segment tree where the nodes hierarchically encode intervals using bit-strings. Given a multi-set of intervals, their intersection is captured by certain equality conditions on the encoding of the nodes. Following that, it turns out that the problem of evaluating an IJQ on an input database containing intervals can be reduced to the problem of evaluating a union of CQs on a database containing scalars and vice versa. Such reductions lead to upper and lower bounds for the data complexity of Boolean IJQs, given upper and lower bounds for the data complexity Boolean CQs. The upper bounds are obtained using a reduction called forward reduction, which reduces any Boolean IJQ to a disjunction of Boolean CQs. The lower bounds are obtained by a reduction called backward reduction, in which any Boolean CQ from the aforementioned disjunction is reduced to the input Boolean IJQ. Overall, the two findings suggest that a Boolean IJQ is as difficult as the forward disjunctions' most difficult Boolean CQ. Last but not least, this thesis identifies an interesting subclass of Boolean IJQs that admit quasi-linear time computation in data complexity. They are referred to as $\iota$-acyclic IJQs