Indexing Network Voronoi Diagrams ⋆ Ugur Demiryurek, and Cyrus Shahabi University of Southern California Department of Computer Science Los Angeles, CA 90089-0781 [demiryur, shahabi]@usc.edu Abstract. The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to effi- ciently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully uti- lize the network Voronoi diagram as a way to partition the space for their specific problems, there is little emphasis on how to efficiently find and access the network Voronoi cell containing a particular point or edge of the network. In this paper, we study the index structures on network Voronoi diagrams that enable exact and fast response to contain query in road networks. We show that existing index struc- tures, treating a network Voronoi cell as a simple polygon, may yield inaccurate results due to the network topology, and fail to scale to large networks with numer- ous Voronoi generators. With our method, termed Voronoi-Quad-tree (or VQ-tree for short), we use Quad-tree to index network Voronoi diagrams to address both of these shortcomings. We demonstrate the efficiency of VQ-tree via experimental evaluations with real-world datasets consisting of a variety of large road networks with numerous data objects. 1 Introduction The latest developments in wireless technologies as well as the widespread use of GPS- enabled mobile devices have led to the recent prevalence of location-based services. An important class of location based queries consists of proximity queries such as k Nearest Neighbor(kNN) query [15, 32, 21, 6, 7] and its variations, e.g., Reverse k Nearest Neighbor (RkNN) [23, 29], k Aggregate Nearest Neighbor (kANN) [28]. The proximity queries in general search for data objects that minimize a distance-based function with reference to one or more query objects. With proximity queries, potentially the distance between the query point and every object in the database (e.g., all the points-of-interest) must be computed in order to find the closest (or the k closest) object(s) to the query point. Hence, the main research focus has been on indexing the objects to avoid the exhaustive search. Earlier studies assumed Euclidean distance as the distance function and hence indexed the objects in Euclidean space (e.g., [32, 30, 21, 24]) using R-tree [4] like index structures. With the advent of online mapping systems such as Google Maps and Mapquest and the availability of accurate ⋆ This research has been funded in part by NSF grants IIS-0238560 (PECASE), IIS-0534761,IIS- 0742811 and CNS-0831505 (CyberTrust), and in part from the METRANS Transportation Center, under grants from USDOT and Caltrans.Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We thank Prof. Ulrich Neumann for his insightful discussions and comments.