Efficient Evaluation of k-Range Nearest Neighbor Queries in Road Networks Jie BaoChi-Yin ChowMohamed F. Mokbel Department of Computer Science and Engineering University of Minnesota – Twin Cities Wei-Shinn Ku Department of Computer Science and Software Engineering Auburn University

2 What is Range NN Queries k-Range NN Queries in Euclidean Space –Given a spatial region, find the k nearest objects to every points within the region –E.g., Find the nearest hotel to a shopping mall k-Range NN Queries in Road Networks –Given a set of road segments, find the k nearest objects to every points on the road segments Region

3 Usages of Range NN Queries Uncertain locations –Measurement imprecision - due to the limitation of the underlying positioning techniques, e.g., 2G/3G and Wi-Fi –Sampling imprecision - due to continuous motion, network delays, and location update frequency Privacy-preserving queries –Users do not want to reveal their exact location information to service providers –Their locations are blurred into spatial areas iPhone's 3G Positioning 5-Anonymous Area

4 Related Works for k-RNN Queries K-Nearest Neighbor in Road Networks –Query processing with pre-computed information Incremental Network Expansion (INE): a best first expansion over the road networks [Papadias et al., VLDB 2003] –Query processing with pre-computed information Use extra pre-computed quad-tree indexes to calculate the distances [Samet et al., SIGMOD 2008] K-Range Nearest Neighbor in Euclidean Space –Pre-computed Voironi Diagrams [Chow et al., SSTD 2009] K-Range Nearest Neighbor in Road Networks –Range Query + INE for every boundary node [Wang and Liu, PVLDB 2009]

5 Motivating Example Computational redundancy in the existing solution –Range Query + Multiple kNN Queries [Wang and Liu, PVLDB 2009] Total number of road segments searched: = 17 Total number of the road segments in the map: 6 Redundancy ratio: (17 - 6) / 6 = 183% (Worse if more boundary points) Can we provide the results without the computational redundancy? Range Search k-NN for D k-NN for B k-NN for F

6 Problem Definition Given: –A undirected graph G=(V, E) as road networks –Set of objects O –A query region R (a set of road segments) –A K value Find: –Answer set A from O such that A contains the K- nearest objects of every point in R based on the network distance in G Objective: –Provide A without computational redundancy

7 Efficient k-RNN Query Processing Step 1: Inside Query Step Step 2: Outside Network Expansion Step –Multiple searching queues –Stop after closest node is searched –Switch to the queue with the smallest searched distance –Termination condition: covers the distance of its k th object Example 2-RNN A B P1P2 P3 1 st iteration Search from A Answer Set P1, P2 2 nd iteration Search from B Answer Set P1, P2 3 rd iteration Search from C Answer Set P1, P2 4 th iteration Search from C Answer Set P1, P2, P3 5 th iteration Search from B Answer Set P1, P2, P3 C Road Segment Set (Range)

8 Distance Calculation Case 1: By a pre-computed shortest path table –Fast but more storage Case 2: Calculation on the fly –Keep the distance information as the searching expands Tradeoff between storage and speed ABE A012 B103 E230 C D P1 P2 ABE A012 B103 E230 C345 D P1 P2 ABE A012 B103 E230 C325 D P1214 P2 Search collision! ABE A012 B103 E230 C325 D546 P1214 P2435

9 Experimental Results ParametersDefault Value Range K value10 1 to 20 Number of Objects to 1000 Query region size (ratio over total space) to Evaluate our algorithm without pre-computed results (KRNN-E), with pre-computed results (KRNN-F) Baseline algorithm: [Wang and Liu, PVLDB 2009] Road networks (Hennepin county, Minnesota, US) 39,513 nodes and 54,444 road segments Parameter settings

10 Comparison with baseline(1/2) a)Impact of different k values b)Impact of different total objects on the map c)Impact of different query region size

11 Comparison with baseline(2/2) Impact of different distribution of the data objects –Uniform distribution –Normal distribution SD is the standard deviation to simulate the hot spot locations like downtown area

12 Tradeoff between storage and performance Tuning parameter P –The percentage of the shortest distance table –Warm up process with 1000 k-RNN queries –Full size of the table is 980 MB

13 Conclusion An efficient algorithm for k-Range Nearest Neighbor (k-RNN) queries in road networks without computational overhead Experiment evaluation –Our solution outperforms the baseline algorithm –Tuning parameter P achieves a tradeoff Privacy preserved applications Uncertain locations

14 Q&A