Visual exploration of spatial data relies heavily on spatial aggregation queries that slice and summarize the data over different regions. These queries comprise computationally-intensive point-inpolygon tests that associate data points to polygonal regions, challenging the responsiveness of visualization tools. This challenge is compounded by the sheer amounts of data, requiring a large number of such tests to be performed. Traditional pre-aggregation approaches are unsuitable in this setting since they fix the query constraints and support only rectangular regions. On the other hand, query constraints are defined interactively in visual analytics systems, and polygons can be of arbitrary shapes. In this paper, we convert a spatial aggregation query into a set of drawing operations on a canvas and leverage the rendering pipeline of the graphics hardware (GPU) to enable interactive response times. Our technique trades-off accuracy for response time by adjusting the canvas resolution, and can even provide accurate results when combined with a polygon index. We evaluate our technique on two large real-world data sets, exhibiting superior performance compared to index-based approaches.
The majority of spatial processing techniques rely heavily on approximating each group of spatial objects by their minimum bounding box (MBB). As each MBB is compact to store (requiring only two multi-dimensional points) and intersection tests between MBBs are cheap to execute, these approximations are used predominantly to perform the (initial) filtering step of spatial data processing. However, fitting (groups of) spatial objects into a rough box often results in a very poor approximation of the underlying data. The resulting MBBs contain a lot of "dead space"-fragments of bounded area that contain no actual objects-that can significantly reduce the filtering efficacy. This paper introduces the general concept of a clipped bounding box (CBB) that addresses the principal disadvantage of MBBs, their poor approximation of spatial objects. Essentially, a CBB "clips away" dead space from the corners of an MBB by storing only a few auxiliary points. On four popular R-tree implementations (a ubiquitous application of MBBs), we demonstrate how minor modifications to the query algorithm exploit auxiliary CBB points to avoid many unnecessary recursions into dead space. Extensive experiments show that clipped R-tree variants substantially reduce I/Os: e.g., by clipping the state-of-the-art revised R*-tree we can eliminate on average 19% of I/Os.
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Sketches are a popular approximation technique for large datasets and high-velocity data streams. While custom FPGA-based hardware has shown admirable throughput at sketching, the state-of-the-art exploits data parallelism by fully replicating resources and constructing independent summaries for every parallel input value. We consider this approach pessimistic, as it guarantees constant processing rates by provisioning resources for the worst case. We propose a novel optimistic sketching architecture for FPGAs that partitions a single sketch into multiple independent banks shared among all input values, thus significantly reducing resource consumption. However, skewed input data distributions can result in conflicting accesses to banks and impair the processing rate. To mitigate the effect of skew, we add mergers that exploit temporal locality by combining recent updates. Our evaluation shows that an optimistic architecture is feasible and reduces the utilization of critical FPGA resources proportionally to the number of parallel input values. We further show that FPGA accelerators provide up to 2.6 x higher throughput than a recent CPU and GPU, while larger sketch sizes enabled by optimistic architectures improve accuracy by up to an order of magnitude in a realistic sketching application.
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