Regular Paper

The VLDB Journal

, Volume 22, Issue 3, pp 319-344

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

UV-diagram: a voronoi diagram for uncertain spatial databases

  • Xike XieAffiliated withDepartment of Computer Science, Aalborg University
  • , Reynold ChengAffiliated withDepartment of Computer Science, The University of Hong Kong Email author 
  • , Man Lung YiuAffiliated withDepartment of Computing, Hong Kong Polytechnic University
  • , Liwen SunAffiliated withUniversity of California
  • , Jinchuan ChenAffiliated withKey Lab for Data Engineering and Knowledge Engineering, MOE. Renmin University of China


The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the Uncertain-Voronoi diagram (or UV-diagram), which divides the data space into disjoint “UV-partitions”. Each UV-partition \(P\) is associated with a set \(S\) of objects, such that any point \(q\) located in \(P\) has the set \(S\) as its nearest neighbor with nonzero probabilities. The UV-diagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point \(q\). It supports “continuous nearest-neighbor search”, which refreshes the set of NN objects of \(q\), as the position of \(q\) changes. It also allows the analysis of nearest-neighbor information, for example, to find out the number of objects that are the nearest neighbors of any point in a given area. A UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation of a UV-diagram, by using a set of UV-cells. A UV-cell of an object \(o\) is the extent \(e\) for which \(o\) can be the nearest neighbor of any point \(q \in e\). We study how to speed up the derivation of UV-cells by considering its nearby objects. We also use the UV-cells to design the UV-index, which supports different queries, and can be constructed in polynomial time. We have performed extensive experiments on both real and synthetic data to validate the efficiency of our approaches.


Voronoi diagram Uncertain data Nearest-neighbor query