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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

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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

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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

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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]

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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14 Q&A

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