Multi-Source Spatial Entity Linkage

Besides the traditional cartographic data sources, spatial information can also be derived from location-based sources. However, even though different location-based sources refer to the same physical world, each one has only partial coverage of the spatial entities, describe them with different attributes, and sometimes provide contradicting information. Hence, we introduce the spatial entity linkage problem, which finds which pairs of spatial entities belong to the same physical spatial entity. Our proposed solution (QuadSky) starts with a time-efficient spatial blocking technique (QuadFlex), compares pairwise the spatial entities in the same block, ranks the pairs using Pareto optimality with the SkyRank algorithm, and finally, classifies the pairs with our novel SkyEx-* family of algorithms that yield 0.85 precision and 0.85 recall for a manually labeled dataset of 1,500 pairs and 0.87 precision and 0.6 recall for a semi-manually labeled dataset of 777,452 pairs. Moreover, we provide a theoretical guarantee and formalize the SkyEx-FES algorithm that explores only 27% of the skylines without any loss in F-measure. Furthermore, our fully unsupervised algorithm SkyEx-D approximates the optimal result with an F-measure loss of just 0.01. Finally, QuadSky provides the best trade-off between precision and recall, and the best F-measure compared to the existing baselines and clustering techniques, and approximates the results of supervised learning solutions

Discretization of Planar Geometric Cover Problems

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union of the translates in the collection contains all the points in $P$. We show that the geometric cover problem can be converted to a form of the geometric set cover, which has a given finite-size collection of translates rather than the infinite continuous solution space of the former. We propose a reduced finite solution space that consists of distinct canonical translates and present polynomial algorithms to find the reduce solution space for disks, convex/non-convex polygons (including holes), and planar objects consisting of finite Jordan curves.Comment: 16 pages, 5 figure