Spatial Databases
| Spacial Databases description |
Chang-Tien Lu Northern Virginia Center
Associate Professor
| Office: | 310 Northern Virginia Center |
|---|---|
| Email: | ctlu@vt.edu |
| Phone: | (703) 538-8373 |
| Website: | http://people.cs.vt.edu/~ctlu |
| Office Hours: | Tu 3-4PM, W 10-11AM |
|---|
2012
Polys, N.,
"Publishing the Greatest Common Denominator",
CEUR-WS, vol. 869, no. Proceedings of the 1st International Workshop on Declarative 3D for the Web Architecture (Dec3D 2012 @ WWW 2012), Lyon, Fr, CEUR-WS, 2012.
Phillips, R. D., L. T. Watson, R. H. Wynne, and N. Ramakrishnan,
"Continuous iterative guided spectral class rejection classification algorithm",
IEEE Trans. Geoscience Remote Sensing, vol. 50, pp. 2303--2317, 2012.
2011
DosSantos, R. F., A. Boedihardjo, and C. T. Lu,
"A Framework for the Expansion of Spatial Features Based on Semantic Footprints",
Proceedings of the 2011 IEEE International Conference on Systems, Man, and Cybernetics (IEEE SMC 2011), Anchorage, Alaska, pp. 3421-3426, 10/2011.
2010
Dai, J., and C. T. Lu,
"C3: Concurrency Control on Continuous Queries over Moving Objects",
Proceedings of the 26th IEEE International Conference on Data Engineering (ICDE-2010), Long Beach, California, pp. 121-132, 03/2010.
2009
Lu, C. T., A. Boedihardjo, and S. Shekhar,
"Analysis of Highway Traffic Data Warehouse with Map Cubes: Highway Traffic Data",
chapter in Geographic Data Mining and Knowledge Discovery (2nd edition), Harvey J. Miller and Jiawei Han (eds.), Taylor and Francis, pp. 69-97, 2009.
2008
Dai, J., and C. T. Lu,
"Concurrency Control for Spatial Access Method",
Encyclopedia of Geographical Information Science, Shashi Shekhar and Hui Xiong (eds.), pp. 124-128, 2008.
DosSantos, R., and C. T. Lu,
"Geography Markup Language",
Encyclopedia of Geographical Information Science, Shashi Shekhar and Hui Xiong (eds.),, pp. 364-368, 2008.
Chen, F., and C. T. Lu,
"Nearest Nearby Query",
Encyclopedia of Geographical Information Science, Shashi Shekhar and Hui Xiong (eds.), pp. 776-782, 2008.
Kou, Y., and C. T. Lu,
"Spatial Outlier Detection",
Encyclopedia of Geographical Information Science, Shashi Shekhar and Hui Xiong (eds.), pp. 832-838, 2008.
Steel, C., and C. T. Lu,
"Impersonator Identification through Dynamic Fingerprinting",
Digital Investigation, the International Journal of Digital Forensics & Incident Response, Elsevier, 2008.
Chang, D., C. T. Lu, Y. Kou, and F. Chen,
"On Detecting Spatial Outliers",
GeoInformatica, An International Journal on Advances of Computer Science for Geographic Information System, Springer, 2008.
Lu, C. T., A. Boedihardjo, J. Dai, and F. Chen,
"HOMES: Highway Operations Monitoring and Evaluation System",
Proceedings of the 16th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Irvine, CA, ACM, pp. 529-530, 11/2008.
2007
Mishra, D., C. A. Shaffer, N. Ramakrishnan, L. T. Watson, K. K. Bae, J. He, A. A. Verstak, and W. H. Tranter,
"S4W: a problem-solving environment for wireless system design",
Software: Practice & Experience, vol. 37, no. 14, New York, NY, USA, John Wiley & Sons, Inc., pp. 1539–1558, 2007.
Lu, C. T., Y. Kou, J. Zhao, and L. Chen,
"Detecting and Tracking Region Outliers in Meteorological Data",
Information Sciences Journal, Informatics and Computer Science Intelligent Systems Applications, An International Journal, Elsevier, vol. 177, no. 7, 2007.
Lu, C. T., D. R. F. Santos, L. Sripada, and Y. Kou,
"Advances of GML for Geospatial Applications",
GeoInformatica: An International Journal on Advances of Computer Science for Geographic Information System, vol. 11, no. 1, pp. 131-157, March, 2007.
Dai, J., and C. T. Lu,
"CLAM: Concurrent Location Management for Moving Objects",
Proceedings of the 15th International Symposium on Advances in Geographic Information Systems, Seattle Washington, Nov, 2007.
Kou, Y., C. T. Lu, and R. F. DosSantos,
"Spatial Outlier Detection: A Graph-based Approach",
Proceedings of the 19th International Conference on Tools with Artificial Intelligence, Sacramento, Patras, Greece, Oct, 2007.
2006
Jefferson, K., C. T. Lu, X. Li, T. C. Hsu, and T. F. Chu,
"The Case for Using Spatiotemporal Traffic Data for Transportation Network Management",
Managing Travel for Planned Special Events: Tools for Practitioners, Newport Beach, California, Nov/Dec, 2006.
Lu, C. T., A. P. Boedihardjo, and J. Zheng,
"Towards an Advanced Spatial-Temporal Visualization System for the Metropolitan Washington, D.C.",
the 2006 TRB International Visualization in Transportation Symposium and Workshop, Denver, Colorado, October, 2006.
Boedihardjo, A., and C. T. Lu,
"AOID: Adaptive Online Incident Detection System",
the 9th International IEEE Conference on Intelligent Transportation Systems, September, 2006.
Lu, C. T., and A. P. Boedihardjo,
"Advanced Traffic Visualization and Mining System",
the 12th Annual ITSVA (Intelligent Transportation Society of Virginia) Conference & Exhibition, Arlington, VA, June, 2006.
Kou, Y., C. T. Lu, and D. Chen,
"Spatial Weighted Outlier Detection",
the 2006 SIAM Conference on Data Mining, Bethesda, Maryland, April, 2006.
Jin, Y., J. Dai, and C. T. Lu,
"Spatial-Temporal Data Mining in Traffic Incident Detection",
the 2006 SIAM Conference on Data Mining, Workshop on Spatial Data Mining, Bethesda, Maryland, April, 2006.
Lu, C. T., A. P. Boedihardjo, and J. Zheng,
"AITVS: Advanced Interactive Traffic Visualization System",
Proceedings of the 22nd International Conference on Data Engineering, Atlanta, GA, pp. 167- 168, April, 2006.
2005
Nambiar, S., and C. T. Lu,
"M-Payment Solutions and M-Commerce Fraud Management",
chapter in Advances in Security and Payment Methods for Mobile, Wen-Chen Hu, Chung-wei Lee, and Weidong Kou (eds.), pp. 192-213, 2005.
Lu, C. T., L. Sripada, S. Shekhar, and R. Liu,
"Transportation Data Visualization and Mining for Emergency Management",
International Journal of Critical Infrastructures, Inderscie, vol. 1, no. 2/3, pp. 170-194, 2005.
Kou, Y., C. T. Lu, A. Godrej, T. Grizzard, and H. Post,
"A Web-based Data Visualization and Analysis System for Watershed Management",
Journal of Geographic Information Science Special Issue on Distributed GIS, vol. 11, no. 1, pp. 40-49, June, 2005.
Lu, C. T., J. Zheng, and K. Jefferson,
"Cubeview: A Web-based Visualization Tool for Intelligent Transportation Systems",
ITS Virginia Journal, March, 2005.
Shekhar, S., S. Chawla, S. Ravada, A. Fetterer, X. Liu, and C. T. Lu,
"Spatial Databases – Accomplishments and Research Needs",
IEEE Transactions on Knowledge and Data Engineering, vol. 11, no. 1, pp. 45-55, Jan/Feb, 2005.
Lu, C. T., A. P. Boedihardjo, and P. Manalwar,
"Exploiting Efficient Data Mining Techniques to Enhance Intrusion Detection Systems",
Proceedings of the 2005 IEEE International Conference on Information Reuse and Integration (IEEE IRI-2005 Knowledge Acquisition and Management), Las Vegas, Nevada, pp. 512-517, August, 2005.
Mathuria, J., C. T. Lu, and J. Dai,
"An Efficient Data Model for Sensor Networks",
the 1st International Workshop on Data Mining, the 7th Joint Conference on Information Sciences, Salt Lake City, Utah, July, 2005.
Fan, W., J. Mathuria, and C. T. Lu,
"Making Data Mining Models Useful to Model Non-paying Customers of Exchange Carriers",
Proceedings of the 2005 SIAM International Conference on Data Mining, Newport Beach, CA, pp. 486-490, April, 2005.
Lu, C. T., and Y. Kou,
"A Web-based Data Analysis System for Watershed Management",
the 2005 Annual Meeting of the Associate of American Geographers(AAG), Denver, Colorado, April, 2005.
2004
Skidmore, R. R., A. Verstak, N. Ramakrishnan, T. S. Rappaport, L. T. Watson, J. He, S. Varadarajan, C. A. Shaffer, J. Chen, K. K. Bae, et al.,
"Towards integrated PSEs for wireless communications: experiences with the S4W and SitePlanner\textregistered projects",
SIGMOBILE Mob. Comput. Commun. Rev., vol. 8, no. 2, New York, NY, USA, ACM, pp. 20–34, 2004.
Lu, C. T., D. Chen, and Y. Kou,
"Multivariate Spatial Outlier Detection",
International Journal on Artificial Intelligence Tools, vol. 13, no. 4, pp. 801-812, December, 2004.
Huang, Y. P., G. L. Guo, and C. T. Lu,
"Using Back Propagation Model to Design a MIDI Music Classification System",
Proceedings of the International Computer Symposium, Taipei, Taiwan, pp. 253- 258, Dec, 2004.
Lu, C. T., and L. R. Liang,
"Wavelet Fuzzy Classification for Detecting and Tracking Region Outliers in Meteorological Data",
Proceedings of the 12th International Symposium on Advances in Geographic Information Systems, Washington DC,, pp. 258-265, Nov., 2004.
Nambiar, S., C. T. Lu, and L. R. Liang,
"Analysis of Payment Transaction Security in Mobile Commerce",
Proceedings of the 2004 IEEE International Conference on Information Reuse and Integration (IEEE IRI-2004), Las Vegas, Nevada, pp. 475-480, Nov, 2004.
Sripada, L., C. T. Lu, and W. Wu,
"Evaluating GML Support for Spatial Databases",
L. Sripada, C.T. Lu, W. Wu, “Evaluating GML Support for Spatial Databases,” Proceedings of the Twenty-Eighth Annual International Computer, Software & Applications Conference (COMPSAC 04), Workshop on Geographic and Biological Data Management(GBDM’ 04), Hong Kong, China, pp. 74-78, September, 2004.
Kou, Y., C. T. Lu, S. Sirwongwattana, and Y. P. Huang,
"Survey of Fraud Detection Techniques",
Proceedings of the 2004 IEEE International Conference on Networking, Sensing, and Control, Taipei, Taiwan, pp. 749-754, 2004.
2003
Rubin, E. J., C. A. Shaffer, N. Ramakrishnan, L. T. Watson, R. Dymond, D. Kibler, R. Dietz, J. Chanat, V. Lohani, D. Bosch, et al.,
"From Landscapes to Waterscapes: A PSE for Landuse Change Analysis",
Engineering with Computers, vol. 19, no. 1, pp. 9–25, July, 2003.
Shekhar, S., C. T. Lu, and P. Zhang,
"A Unified Approach to Spatial Outliers Detection",
GeoInformatica, An International Journal on Advances of Computer Science for Geographic Information System, vol. 7, no. 2, pp. 139-166, June, 2003.
Lu, C. T., D. Chen, and Y. Kou,
"Algorithms for Spatial Outlier Detection",
Proceedings of 3rd International Conference on Data Mining, Melbourne, Florida, pp. 597-600, Nov, 2003.
Zhao, J., C. T. Lu, and Y. Kou,
"Detecting Region Outliers in Meteorological Data",
Proceedings of the 11th International Symposium on Advances in Geographic Information Systems, New Orleans, Louisiana, pp. 49-55, Nov, 2003.
Lu, C. T., D. Chen, and Y. Kou,
"Detecting Spatial Outliers with Multiple Attributes",
Proceedings of the 15th International Conference on Tools with Artificial Intelligence, Sacramento, California, pp. 122-128, Nov, 2003.
Lu, C. T., Y. Kou, H. Wang, S. Shekhar, P. Zhang, and R. Liu,
"Two Web-Based Spatial Data Visualization and Mining Systems: Mapcube & Mapview",
Proceedings of the International Workshop on Next Generation Geospatial Information, National Science Foundations, Cambridge(Boston), Massachusetts, October, 2003.
Zhao, J., C. T. Lu, and Y. Kou,
"Chang Detection in Meteorological Data",
Proceedings of the 7th Joint Conference on Information Sciences, Research Triangle Park, North Carolina, pp. 509-512, Sep, 2003.
2002
Watson, L. T., V. K. Lohani, D. F. Kibler, R. L. Dymond, N. Ramakrishnan, and C. A. Shaffer,
"Integrated Computing Environments for Watershed Management",
ASCE Journal of Computing in Civil Engineering, vol. 16, no. 4, pp. 259–268, October, 2002.
Shekhar, S., C. T. Lu, S. Chawla, and S. Ravada,
"Efficient Join Index Based Join Processing",
IEEE Transactions on Knowledge and Data Engineering, vol. 14, no. 6, pp. 1400-1421, Nov/Dec, 2002.
Shekhar, S., C. T. Lu, and P. Zhang,
"Detecting Graph-based Spatial Outliers",
International Journal of Intelligent Data Analysis, vol. 6, no. 3, pp. 451-468, 2002.
Shekhar, S., C. T. Lu, P. Zhang, and R. Liu,
"Data Mining for Visualization of Large Spatial Datasets",
Proceedings of the 14th IEEE International Conference On Tools with Artificial Intelligence, Washington DC, pp. 41-48, November, 2002.
Shekhar, S., C. T. Lu, R. Liu, and C. Zhou,
"CubeView: A System for Traffic Data Visualization",
Proceedings of the IEEE 5th International Conference on Intelligent Transportation Systems, Singapore, pp. 674-678, September , 2002.
2001
Shekhar, S., C. T. Lu, X. Tan, and S. Chawla,
"Map Cube: A Visualization Tool for Spatial Data Warehouses",
chapter in Geographic Data Mining and Knowledge Discovery, Harvey J. Miller and Jiawei Han (eds.), pp. 74-109, 2001.
Shekhar, S., Y. Huang, W. Wu, C. T. Lu, and S. Chawla,
"What's Spatial About Spatial Data Mining: Three Case Studies",
chapter in Data Mining for Scientific and Engineering Applications, R. Grossman, C. Kamath, V. Kumar, R. Namburu (eds.), 2001.
Shekhar, S., C. T. Lu, and P. Zhang,
"Detecting Graph-based Spatial Outliers: Algorithms and Applications",
Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 365-370, August, 2001.
1999
Shekhar, S., C. T. Lu, X. Tan, and S. Chawla,
"Map Cube: A Visualization Tool for Spatial Data Warehouses - A Summary of Results",
NSF Workshop on Data Mining in GIS, March, 1999.
Shekhar, S., S. Chawla, S. Ravada, A. Fetterer, X. Liu, and C. T. Lu,
"Spatial Databases –Accomplishments and Research Needs",
IEEE Transactions on Knowledge and Data Engineering, vol. 11, no. 1, pp. 45-55, 02/1999.
1998
Ravada, S., S. Shekhar, C. T. Lu, and S. Chawla,
"Optimizing Join Index Based Join Processing",
Proceedings of the 17th IEEE Symposium on Reliable Distributed Systems, West Lafayette, Indiana, pp. 302-310, October, 1998.
1994
Pemmaraju, S. V., and C. A. Shaffer,
"Analysis of the worst case space complexity of a PR quadtree",
Inf. Process. Lett., vol. 49, no. 5, Amsterdam, The Netherlands, The Netherlands, Elsevier North-Holland, Inc., pp. 263–267, 1994.
Shaffer, C. A., J. M. A. Begole, J. L.W. Carstensen, R. W. Morrill, and E. A. Fox,
"GeoSim: A GIS-Based Simulation Laboratory for Introductory Geography",
Proceedings of the 1994 ADCIS Conference, February, 1994.
1993
L.W. Carstensen, J., C. A. Shaffer, R. W. Morrill, and E. A. Fox,
"GeoSim: A GIS-Based Simulation Laboratory for Introductory Geography",
Journal of Geography, vol. 92, no. 5, pp. 217–222, September/Octobe, 1993.
Shaffer, C. A., R. Juvvadi, and L. S. Heath,
"A Generalized Comparison of Quadtree and Bintree Storage Requirements",
Image and Vision Computing, vol. 11, no. 7, pp. 402–412, September, 1993.
Shaffer, C. A., and P. R. Brown,
"A Paging Scheme for Pointer-Based Quadtrees",
SSD '93: Proceedings of the Third International Symposium on Advances in Spatial Databases, London, UK, Springer-Verlag, pp. 89–104, 1993.
1992
Shaffer, C. A., and G. M. Herb,
"A Real-Time Robot Arm Collision Avoidance System",
IEEE Transactions on Robotics, vol. 8, no. 2, pp. 149–160, 1992.
Shaffer, C. A.,
Data representations for Geographic Information Systems,
, vol. 27, Medford, NJ, American Society for Information Science, pp. 135–172, 1992.
Shaffer, C. A., and C. D. Feustel,
Exact computation of 2–D intersections,
, San Diego, CA, USA, Academic Press Professional, Inc., pp. 188–192, 1992.
Shaffer, C. A., and M. T. Ursekar,
"Large Scale Editing and Vector to Raster Conversion Via Quadtree Spatial Indexing",
Proceedings of the 5th International Symposium on Spatial Data Handling, pp. 505–513, August, 1992.
Pemmaraju, S. V., and C. A. Shaffer,
Analysis of the Worst Case Space Complexity of a PR Quadtree,
, Blacksburg, VA, USA, Virginia Polytechnic Institute && State University, 1992.
1991
Shaffer, C. A.,
"Real-time robot arm collision detection for telerobotics",
Comput. Electr. Eng., vol. 17, no. 3, Tarrytown, NY, USA, Pergamon Press, Inc., pp. 205–215, 1991.
Shaffer, C. A., and Q. F. Stout,
"Linear time distance transforms for quadtrees",
CVGIP: Image Underst., vol. 54, no. 2, Orlando, FL, USA, Academic Press, Inc., pp. 215–223, 1991.
Lattanzi, M. R., and C. A. Shaffer,
"An optimal boundary to quadtree conversion algorithm",
CVGIP: Image Underst., vol. 53, no. 3, Orlando, FL, USA, Academic Press, Inc., pp. 303–312, 1991.
,
"Getting Around on a Sphere",
Graphics Gems II, San Diego, CA, USA, Academic Press Professional, Inc., 1991.
Brown, P. R., C. A. Shaffer, and R. E. Webber,
"A paging scheme for pointer-based quadtrees",
CSC '91: Proceedings of the 19th annual conference on Computer Science, New York, NY, USA, ACM, pp. 687, 1991.
Shaffer, C. A., and C. D. Feustel,
A Representation and Algorithm for Exact Computation of Cascaded Polygon Intersections with Fixed Storage Requirements,
, Blacksburg, VA, USA, Virginia Polytechnic Institute && State University, 1991.
Shaffer, C. A., L. W. Carstensen, V. F. Miranda, S. A. Kriss, R. W. Morrill, and E. A. Fox,
Project GEOSIM: The First Two Modules,
, Blacksburg, VA, USA, Virginia Polytechnic Institute && State University, 1991.
1990
Oskard, D. N., T. - H. Hong, and C. A. Shaffer,
"Real-Time Algorithms and Data Structures for Underwater Mapping",
IEEE Transactions on Systems, Man, and Cybernetics, vol. 20, no. 6, pp. 1469–1475, November/Decembe, 1990.
Shaffer, C. A., H. Samet, and R. C. Nelson,
"QUILT: A Geographic Information System Based on Quadtrees",
International Journal of Geographic Information Systems, vol. 4, no. 2, pp. 103–131, 1990.
Ang, C. - H., H. Samet, and C. A. Shaffer,
"A New Region Expansion for Quadtrees",
IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7, Washington, DC, USA, IEEE Computer Society, pp. 682–686, 1990.
Shaffer, C. A.,
Fast circle-rectangle intersection checking,
, San Diego, CA, USA, Academic Press Professional, Inc., pp. 51–53, 1990.
Shaffer, C. A.,
"A full resolution elevation representation requiring three bits per pixel",
SSD '90: Proceedings of the first symposium on Design and implementation of large spatial databases, New York, NY, USA, Springer-Verlag New York, Inc., pp. 45–64, 1990.
Shaffer, C. A., and D. B. Boldery,
The Elevation Pyramid,
, Blacksburg, VA, USA, Virginia Polytechnic Institute & State University, 1990.
1988
Oskard, D. N., T. - H. Hong, and C. A. Shaffer,
"Real-Time Algorithms and Data Structures for Underwater Mapping",
SPIE Symposium on Sensor Fusion: Spatial Reasoning and Scene Interpretation, November, 1988.
Ang, C. - H., H. Samet, and C. A. Shaffer,
"Fast Region Expansion for Quadtrees",
Proceedings of the Third International Symposium on Spatial Data Handling, pp. 19–38, August, 1988.
1986
Shaffer, C. A.,
Application of alternative quadtree representations,
, College Park, MD, USA, University of Maryland at College Park, 1986.
Shaffer, C. A.,
"An Empirical Comparison of Vectors, Rasters, and Quadtrees for Representing Geographic Data",
Proceedings of the International Colloquium on the Construction and Display of Geoscientific Maps Derived from Databases, Geologisches Jahrbuch A 104, pp. 99–115, December, 1986.
Samet, H., C. A. Shaffer, R. C. Nelson, Y. - G. Huang, K. Fujimura, and A. Rosenfeld,
"Hierarchical Data Structures for Geographic Information",
Proceedings of the International Colloquium on the Construction and Display of Geoscientific Maps Derived from Databases, Geologisches Jahrbuch A 104, pp. 97–98, December, 1986.
Shaffer, C. A., and H. Samet,
"An Optimal Quadtree Construction Algorithm",
Proceedings of the Eighth International Conference on Pattern Recognition, pp. 317–319, October, 1986.
1985
Samet, H., C. A. Shaffer, and R. E. Webber,
"The Segment Quadtree: A Linear Quadtree-Based Representation for Linear Features",
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'85), pp. 385–389, June, 1985.
1984
Samet, H., A. Rosenfeld, C. A. Shaffer, and R. E. Webber,
"Use of Hierarchical Data Structures in Geographical Information Systems",
Proceedings of the International Symposium on Spatial Data Handling, pp. 392–411, August, 1984.
Samet, H., A. Rosenfeld, C. A. Shaffer, and R. E. Webber,
"Processing Geographic Data with Quadtrees",
Proceedings of the Seventh International Conference on Pattern Recognition, pp. 212–215, August, 1984.
1983
Samet, H., A. Rosenfeld, C. A. Shaffer, and R. E. Webber,
"Quadtree Region Representation in Cartography: Experimental Results",
IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 6, pp. 1148–1154, November/Decembe, 1983.
Samet, H., A. Rosenfeld, C. A. Shaffer, and R. E. Webber,
"A Quadtree-Based Geographical Information System",
Proceedings of the Third Scandinavian Conference on Image Analysis, pp. 231–236, July, 1983.
Captop Enhancements: Real-time Traffic Monitoring and Analysis
Granting Institution: District of Columbia
Amount: $223,400
CapTOP Enhancements: Travel Time Display, Patrol AVL and Remote Data Collections
Granting Institution: Department of Transportation, District of Columbia
Amount: $129,900
Efficient and Scalable Design of Archived Data Management System
Granting Institution: $54,216
Amount: Virginia Department of Transportation
Efficient and Scalable Localized Search Engine
Granting Institution: NetRoster Inc.
Amount: $18,337
Intelligent Visualization and Analysis of Traffic Data on the Sun Platform for Transportation Government Agencies
Granting Institution: Sun Microsystems
Amount: $39,975
Real-Time Freeway Performance Monitoring System
Granting Institution: Virginia Department of Transportation
Amount: $221,646
Yellow Button: Creating a Situationally Aware Community through Collective Intelligence
Granting Institution: Virginia’s Center for Innovative Technology
Amount: $52,500