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Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue. The Min-dist Location Selection Query. University of Melbourne 8/08/2014. Outline. Backgrounds Algorithms Sequential Scan Algorithm Quasi-Voronoi Cell Nearest Facility Circle Maximum NFC Distance Experiments Conclusions.
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Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue The Min-dist Location Selection Query University of Melbourne 8/08/2014
Outline • Backgrounds • Algorithms • Sequential Scan Algorithm • Quasi-Voronoi Cell • Nearest Facility Circle • Maximum NFC Distance • Experiments • Conclusions
Motivation • 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
Motivation: urban planning simulation Modeling urban dynamics [1]
Motivation: online computer games An online game example [2] .5.
Problem Definition • 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
Related Work • 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 Qfor a new facility to minimize the average distance between a client and her nearest facility Q
Related Work .8.
Algorithms: Problem Redefinition • Larger distance reduction smaller average client-facility distance • The influence Set of p, IS(p) • • The distance reduction of p, dr(p) IS(p1) IS(p2)
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
Algorithms: Quasi-Voronoi Cell • A potential location’s surrounding existing facilities constraint its search space for IS The Quasi-Voronoi Cell (QVC) [11]
Algorithms: Nearest Facility Circle • 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
Algorithms: Maximum NFC Distance • 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
Algorithms: Maximum NFC Distance • Maximum NFC Distance (MND) • The largest distance between the points on the NFCs and the MBR of a node on the clients
Algorithms: Maximum NFC Distance • Efficient MND Computation • Only requires checking four points per node • The four candidate furthest points (CFP): Iv1, Iv2, Ih1, Ih2
Experiments: settings • 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
Experiments: dataset cardinality MND is as good as NFC in running time and I/O. They both outperform SS and QVC by one order of magnitude.
Experiments: dataset cardinality MND reduces 40% in index size compared to NFC
Experiments: data distribution • Gaussian • Real MND shows the best overall performance
Conclusions • 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
Reference [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.
