Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue The Min-dist Location Selection Query University...
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Transcript of Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue The Min-dist Location Selection Query University...
Jianzhong Qi Rui Zhang Lars Kulik Dan Lin Yuan Xue
The Min-dist Location Selection Query
University of Melbourne18/04/23
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
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
Problem Optim.
Function
Solution
Space
Distance
Function
Datasets
[4] Max-inf Continuous L2 C, F
[5] Max-inf Discrete L2 C, F
[6] Max-inf Continuous L1 C, F
[7] Max-inf Discrete L2 C, P
[8] Max-inf Discrete L2 C, F, P
[3] Min-dist Continuous L1 C, F
[9] Min-dist Continuous Network C, F, E
[10] Min-dist Discrete L2 C, P
Proposed Min-dist Discrete L2 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)c
dist(c,p)facility)exsistingneareastdist(c,c'sdr(p)
IS(p)c facility)exsistingneareastdist(c,c'sdist(c,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
.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
IS(p)c)(cNFCp
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): Iv1, Iv2,
Ih1, Ih2
CFP(N)}|I{dist(I,N) MND(N) max
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
Parameter Value
Disk page size 4KB
Client set size 10K, 50K, 100K, 500K, 1000K
Existing facility set size 0.1K, 0.5K, 1K, 5K, 10K
Potential location set size 1K, 5K, 10K, 50K, 100K
; σ2 (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.
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] 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.