Uncertain Voronoi Cell Computation Based on Space Decomposition [chapter]

Tobias Emrich, Klaus Arthur Schmid, Andreas Züfle, Matthias Renz, Reynold Cheng
2015 Lecture Notes in Computer Science  
The problem of computing Voronoi cells for spatial objects whose locations are not certain has been recently studied. In this work, we propose a new approach to compute Voronoi cells for the case of objects having rectangular uncertainty regions. Since exact computation of Voronoi cells is hard, we propose an approximate solution. The main idea of this solution is to apply hierarchical access methods for both data and object space. Our space index is used to efficiently find spatial regions
more » ... h must (not) be inside a Voronoi cell. Our object index is used to efficiently identify Delauny relations, i.e., data objects which affect the shape of a Voronoi cell. We develop three algorithms to explore index structures and show that the approach that descends both index structures in parallel yields fast query processing times. Our experiments show that we are able to approximate uncertain Voronoi cells much more effectively than the state-of-the-art, and at the same time, improve run-time performance. Simply ignoring these notions of imprecise, obsolete, unreliable and cloaked data, thus pretending that the data is accurate, current, reliable and correct is a common source of false decision making. The research challenge in handling uncertainty in spatial and spatio-temporal data is to obtain reliable results despite the presence of uncertainty. In this work, we revisit the problem of reliably answering nearest-neighbor queries in uncertain data. The problem of finding the closest uncertain object, which has applications such as taxi-customer matching, has gained much attention in recent years [2] [3] [4] [5] . Following a common approach in uncertain data management, these approaches assume that uncertain objects are represented by rectangular or circular uncertainty regions, which are guaranteed to enclose the true (but unknown) position of the respective spatial objects. Following the approach of [6], we carry the concept of Voronoi cells to uncertain data. The idea of [6] is to approximate the possible Voronoi cell V(O) of an object O, which is defined as the space where a query point q can possibly have O as its nearest neighbor. Applications for possible Voronoi cells include geo-location-based services, such as taxi assignments: The possible Voronoi cell of an individual taxi cab c covers the space of a city where customers may possibly have c as their nearest taxi. In such an application, as we see in taxi-GPS data sets such as the T-drive dataset [7, 8] , the GPS position c(t) of a cab c at a time t may be highly obsolete, due to infrequent GPS updates. Models to infer the uncertainty region of a mobile object on a road network given past observations have been given in the literature [9] . As an example of a possible Voronoi cell, consider Figure 1(a) , where rectangles correspond to the uncertainty regions of objects. The highlighted region corresponds to the subspace V(A), for which it holds that any point q ∈ V(A) may possibly have object A as its nearest neighbor, i.e., the possible Voronoi cell of A. Finding this region, which is the goal of this paper, is not a trivial task: The shape of V(A) is a non-convex region Case 1: R is fully contained in S A (B) iff Dom(A, B, R);
doi:10.1007/978-3-319-22363-6_6 fatcat:qc4qudhkavfpvai6namaslel2a