Efficient spatial sampling of large geographical tables

Abstract

Large-scale map visualization systems play an increasingly important role in presenting geographic datasets to end users. Since these datasets can be extremely large, a map rendering system often needs to select a small fraction of the data to visualize them in a limited space. This paper addresses the fundamental challenge of thinning: determining appropriate samples of data to be shown on specific geographical regions and zoom levels. Other than the sheer scale of the data, the thinning problem is challenging because of a number of other reasons: (1) data can consist of complex geographical shapes, (2) rendering of data needs to satisfy certain constraints, such as data being preserved across zoom levels and adjacent regions, and (3) after satisfying the constraints, an optimal solution needs to be chosen based on objectives such as maximality, fairness, and importance of data. This paper formally defines and presents a complete solution to the thinning problem. First, we express the problem as an integer programming formulation that efficiently solves thinning for desired objectives. Second, we present more efficient solutions for maximality, based on DFS traversal of a spatial tree. Third, we consider the common special case of point datasets, and present an even more efficient randomized algorithm. Finally, we have implemented all techniques from this paper in Google Maps [6] visualizations of Fusion Tables [14], and we describe a set of experiments that demonstrate the tradeoffs among the algorithms.

Viewing streaming spatially-referenced data at interactive rates

“…This criteria is a core requirement mentioned in the work of Das Sarma et al [33] from Google. If a geographic window W contains a visible text label R, and another window W ′ , obtained by zooming in, also contains R, then R should also be sampled in W ′ , which means that R should be visible in W ′ .…”

“…Figure 1 gives an example scenario which consists of the task of displaying just 1, 000 text objects in a map. In these circumstances, a subset of objects must be selected from the original dataset to display so that users have a manageable amount of information (a task also known as "spatial sampling" [4] or "thinning" [33]). We use the term layout problem to describe the combined selection and display problem.…”

Multiresolution select-distinct queries on large geographic point sets

“…A similar problem of "thinning" large geographic datasets for display has been defined by Sarma et al [13], which is currently being used to perform spatial sampling by Google Maps. Specifically, they focus on selecting a finite list of features to appear within uniform regions at each zoom level.…”

“…The filters may vary in their selectivity, in the sense that some filters could remove many data entries from being selected into T , while others may have little effect on T because they do not exclude many of the entries. This goal (in combination with the spatial fullness property) precludes the use of some precomputation-based approaches [13].…”

Recent progress towards an ecosystem of structured data on the Web

“…Hence, in the recent months we have launched visualizations such as the zoomable time-line (see Figure 1) and the network graph (see Figure 2). Importantly, the architecture and optimizations we created for map visualizations (e.g., [3]) informed us on how to support other visualizations. The main challenge we had to address is providing an efficient and smooth visualization experience in a cloud-based environment, where users expect immediate responses as they zoom into a visualization or pan across it.…”