Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue The Min-dist Location Selection Query University of Melbourne 14/05/2015

Outline.2.  Backgrounds  Algorithms  Sequential Scan Algorithm  Quasi-Voronoi Cell  Nearest Facility Circle  Maximum NFC Distance  Experiments  Conclusions

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

Motivation: urban planning simulation.4. Modeling urban dynamics [1]

Motivation: online computer games.5. An online game example [2]

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

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

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

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 )

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.11.  A potential location’s surrounding existing facilities constraint its search space for IS The Quasi-Voronoi Cell (QVC) [11]

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 

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

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

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 

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

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.

Experiments: dataset cardinality.18. MND reduces 40% in index size compared to NFC

Experiments: data distribution.19.  Gaussian  Real MND shows the best overall performance

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

Reference.21. [1] [2] [3] D. Zhang, Y. Du, T. Xia, and Y. Tao, “Progressive computation of the min-dist optimal-location query,” in VLDB, [4] S. Cabello, J. M. D´ıaz-B´a˜nez, S. Langerman, C. Seara, and I. Ventura, “Reverse facility location problems.” in CCCG, [5] T. Xia, D. Zhang, E. Kanoulas, and Y. Du, “On computing top-t most influential spatial sites.” in VLDB, [6] Y. Du, D. Zhang, and T. Xia, “The optimal-location query.” in SSTD, [7] Y. Gao, B. Zheng, G. Chen, and Q. Li, “Optimal-location-selection query processing in spatial databases,” TKDE, vol. 21, pp. 1162–1177, [8] J. Huang, Z. Wen, J. Qi, R. Zhang, J. Chen, and Z. He, “Top-k most influential locations selection,” in CIKM, [9] X. Xiao, B. Yao, and F. Li, “Optimal location queries in road network databases,” in ICDE, [10] [11] I. Stanoi, M. Riedewald, D. Agrawal, and A. E. Abbadi, “Discovery of influence sets in frequently updated databases,” in VLDB, [12]

Thank you! Jianzhong Qi