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Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue The Min-dist Location Selection Query University of Melbourne 14/05/2015
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Outline.2. Backgrounds Algorithms Sequential Scan Algorithm Quasi-Voronoi Cell Nearest Facility Circle Maximum NFC Distance Experiments Conclusions
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Motivation.3. The min-dist location selection problem Problem setting: a set of facilities serving a set of clients If we want to set up a new facility, choose a location from a set of potential locations to minimize the average distance between the facilities and the clients Motivating applications Urban planning simulations: deploy public facilities Multiple player online games: place players
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Motivation: urban planning simulation.4. Modeling urban dynamics [1]
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Motivation: online computer games.5. An online game example [2]
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Problem Definition.6. A set of clients, C A set of existing facilities, F A set of potential locations, P Select a potential location for a new facility to minimize the average distance between a client and her nearest facility
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Related Work.7. The min-dist optimal location problem [3] A set of clients C A set of existing facilities F A candidate region Q Compute a location in Q for a new facility to minimize the average distance between a client and her nearest facility Q
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Related Work.8. Location Optimization Problems ProblemOptim. Function Solution Space Distance Function Datasets [4]Max-infContinuousL2L2 C, F [5]Max-infDiscreteL2L2 C, F [6]Max-infContinuousL1L1 C, F [7]Max-infDiscreteL2L2 C, P [8]Max-infDiscreteL2L2 C, F, P [3]Min-distContinuousL1L1 C, F [9]Min-distContinuousNetworkC, F, E [10]Min-distDiscreteL2L2 C, P ProposedMin-distDiscreteL2L2 C, F, P
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Algorithms: Problem Redefinition.9. Larger distance reduction smaller average client-facility distance The influence Set of p, IS(p) The distance reduction of p, dr(p) IS(p 1 ) IS(p 2 )
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Algorithms: Sequential Scan.10. Sequential Scan Algorithm Sequentially check all the potential locations For every potential location p Sequentially check all the clients, compute IS(p) and dr(p) Report the one with the largest dr value Drawback – repeated dataset accesses Key algorithm design considerations Restrict the search space for IS(p) Share the computation for determining the influence sets of multiple potential locations
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Algorithms: Quasi-Voronoi Cell.11. A potential location’s surrounding existing facilities constraint its search space for IS The Quasi-Voronoi Cell (QVC) [11]
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Algorithms: Nearest Facility Circle.12. Constraint the search space from clients’ perspective Nearest facility circle of a client c, NFC(c) An R-tree on the NFCs An R-tree on the potential locations Synchronous traversal
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Algorithms: Maximum NFC Distance.13. An index reduced version of NFC NFC requires two R-trees to index the clients One for the NFCs The other for the clients Inefficient to maintain with clients coming and leaving constantly Key insight Combine two R-trees together A single value to describe a region that encloses the NFCs of the clients in an R-tree node N The Maximum NFC Distance
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Algorithms: Maximum NFC Distance.14. Maximum NFC Distance (MND) The largest distance between the points on the NFCs and the MBR of a node on the clients
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Algorithms: Maximum NFC Distance.15. Efficient MND Computation Only requires checking four points per node The four candidate furthest points (CFP): I v1, I v2, I h1, I h2
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Experiments: settings.16. Hardware 2.66GHz Intel(R) Core(TM)2 Quad CPU,3GB RAM Datasets Synthetic datasets: Uniform, Gaussian, Zipfian Real datasets: populated places and cultural landmarks in US and North America [13] US: |C| = 15206, |F| = 3008, |P| = 3009 NA: |C| = 24493, |F| = 4601, |P| = 4602 ParameterValue Disk page size4KB Client set size10K, 50K, 100K, 500K, 1000K Existing facility set size0.1K, 0.5K, 1K, 5K, 10K Potential location set size1K, 5K, 10K, 50K, 100K ; σ 2 (Gaussian distribution ) 0; 0.125, 0.25, 0,5, 1, 2 N; ∂ (Zipfian distribution)1000; 0.1, 0.3, 0.6, 0.9, 1.2
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Experiments: dataset cardinality.17. MND is as good as NFC in running time and I/O. They both outperform SS and QVC by one order of magnitude.
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Experiments: dataset cardinality.18. MND reduces 40% in index size compared to NFC
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Experiments: data distribution.19. Gaussian Real MND shows the best overall performance
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Conclusions.20. A new location optimization problem Urban simulation Massively multiplayer online games Two approaches from commonly used techniques Quasi-Voronoi Cell Nearest Facility Circle A new approach MND High efficiency No additional index
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Reference.21. [1] http://www.simcenter.org. [2] http://connect.in.com/free-online-games-com/photos-540361-9095265.html. [3] D. Zhang, Y. Du, T. Xia, and Y. Tao, “Progressive computation of the min-dist optimal-location query,” in VLDB, 2006. [4] S. Cabello, J. M. D´ıaz-B´a˜nez, S. Langerman, C. Seara, and I. Ventura, “Reverse facility location problems.” in CCCG, 2005. [5] T. Xia, D. Zhang, E. Kanoulas, and Y. Du, “On computing top-t most influential spatial sites.” in VLDB, 2005. [6] Y. Du, D. Zhang, and T. Xia, “The optimal-location query.” in SSTD, 2005. [7] Y. Gao, B. Zheng, G. Chen, and Q. Li, “Optimal-location-selection query processing in spatial databases,” TKDE, vol. 21, pp. 1162–1177, 2009. [8] J. Huang, Z. Wen, J. Qi, R. Zhang, J. Chen, and Z. He, “Top-k most influential locations selection,” in CIKM, 2011. [9] X. Xiao, B. Yao, and F. Li, “Optimal location queries in road network databases,” in ICDE, 2011. [10] http://www.esri.com/. [11] I. Stanoi, M. Riedewald, D. Agrawal, and A. E. Abbadi, “Discovery of influence sets in frequently updated databases,” in VLDB, 2001. [12] http://www.rtreeportal.org.
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Thank you! Jianzhong Qi jiqi@student.unimelb.edu.au
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