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Ariel Cary, Zhengguo Sun, Vagelis Hristidis, Naphtali Rishe Florida International University School of Computing and Information Sciences 11200 SW 8 th St, Miami, FL 33199 {acary001,sunz,vagelis,rishen}@cis.fiu.edu Sponsored by: NSF Cluster Exploratory (CluE) Experiences on Processing Spatial Data with MapReduce

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Agenda 1. Introduction 2. Solving Spatial Problems in MapReduce R-Tree Index Construction Aerial Image Processing 3. Experimental Results 4. Related Work 5. Conclusion 2 Florida International University

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Introduction Spatial databases mainly store: Raster data (satellite/aerial digital images), and Vector data (points, lines, polygons). Traditional sequential computing models may take excessive time to process large and complex spatial repositories. Emerging parallel computing models, such as MapReduce, provide a potential for scaling data processing in spatial applications. 3 Florida International University

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Introduction (cont.) MapReduce is an emerging massively parallel computing model (Google) composed of two functions: Map: takes a key/value pair, executes some computation, and emits a set of intermediate key/value pairs as output. Reduce: merges its intermediate values, executes some computation on them, and emits the final output. In this work, we present our experiences in applying the MapReduce model to: Bulk-construct R-Trees (vector) and Compute aerial image quality (raster) 4 Florida International University

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Introduction (cont.) Apache's Hadoop Linux operating system XEN hypervisor Hadoop Distributed File System (HDFS) SOCKS proxy server 480 computers (nodes), each half terabytes storage 5 Florida International University

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R-Tree Index Construction Aerial Image Processing 2. Solving Spatial Problems in MapReduce

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MapReduce (MR) R-Tree Construction R-Tree Bulk-Construction Every object o in database D has two attributes: o.id - the objects unique identifier. o.P - the objects location in some spatial domain. The goal is to build an R-Tree index on D. MapReduce Algorithm 1. Database partitioning function computation (MR). 2. A small R-Tree is created for each partition (MR). 3. The small R-Trees are merged into the final R-Tree. 7 Florida International University

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Phase 1 – Partitioning Function – Goal: compute f to assign objects of D into one of R possible partitions s.t.: – R (ideally) equally-sized partitions are generated (minimal variance is acceptable). – Objects close in the spatial domain are placed within the same partition. – Proposed solution: – Use Z-order space-filling curve to map spatial coordinate samples (3%) into an sorted sequence. – Collect splitting points that partition the sequence in R ranges. Where: o is an spatial object in the database. C which is a constant that helps in sending Mappers' outputs to a single Reducer. U is a space-filling curve, e.g. Z-order value. S' is an array containing R-1 splitting points. 8 Florida International University

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Phase 2 - R-Tree Construction in MR Mappers compute f() values for objects. Reducers compute an R-Tree for each group of objects with identical f() value Where: o is an spatial object in the database. f is the partitioning function computed in phase 1. Tree.root is the R-Tree root node. 9 Florida International University

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Phase 3 - R-Tree Consolidation sequential process 10 Florida International University

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Image Processing in MapReduce Aerial Image Quality Computation Let d be a orthorectified aerial photography (DOQQ) file and t be a tile inside d, d.name is ds file name and t.q is the quality information of tile t. The goal is to compute a quality bitmap for d. MapReduce Algorithm A customized InputFormatter partitions each DOQQ file d into several splits containing multiple tiles. The Mappers compute the quality bitmap for each tile inside a split. The Reducers merge all the bitmaps that belongs to a file d and write them to an output file. 11 Florida International University

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Image Processing in MapReduce MapReduce Algorithm Where: d is a DOQQ file. t is a tile in d. t.q is the quality bitmap of t. 12 Florida International University

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3. Experimental Results

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Experimental Results: Setting Data Set Environment The cluster was provided by the Google and IBM Academic Cluster Computing Initiative. The cluster contains around 480 computers running Hadoop - open source MapReduce. 14 Florida International University

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Experimental Results: R-Tree R-Tree Construction Performance Metrics 15 Florida International University

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Experimental Results: R-Tree MapReduce R-Trees vs. Single Process (SP) Objects per ReducerConsolidated R-Tree Data setRAverageStdevNodesHeight FLD25,690,41912,183172,7764 42,845,2106,347172,6244 81,422,6052,235173,1414 16711,3792,533162,5184 32355,6512,379173,2733 64177,8261,816173,4453 SP11,382,1850172,6814 YPD49,257,18822,137568,8544 84,628,5949,413568,7164 162,314,2977,634568,2324 321,157,1496,043567,5504 64578,5742,982566,1994 SP37,034,1260587,3535 16 Florida International University

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Experimental Results: Imagery Tile Quality Computation 17 Florida International University

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4. Related Work

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Related Work Previous works on R-Tree parallel construction faced intrinsic distributed computing problems: load balancing, process scheduling, fault tolerance, etc. Schnitzer and Leutenegger [16] proposed a Master-Client R-Tree, where the data set is first partitioned using Hilbert packing sort algorithm, then the partitions are declustered into a number of processors, where individual trees are built. At the end, a master process combines the individual trees into the final R-Tree. Papadopoulos and Manolopoulos [17] proposed a methodology for sampling-based space partitionining, load balancing, and partition assignment into a set of processors in parallely building R-Trees. 19 Florida International University

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5. Conclusion

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Conclusion We used the MapReduce model to solve two spatial problems on a Google&IBM cluster: (a) Bulk-construction of R-Trees and (b) Aerial image quality computation MapReduce can dramatically improve task completion times. Our experiments show close to linear scalability. Our experience in this work shows MapReduce has the potential to be applicable to more complex spatial problems. 21 Florida International University

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References [1]Antonin Guttman: R-Trees: A Dynamic Index Structure for Spatial Searching. SIGMOD 1984:47- 57. [2]NSF Cluster Exploratory Program: http://www.nsf.gov/pubs/2008/nsf08560/nsf08560.htm [3]Google&IBM Academic Cluster Computing Initiative: http://www.google.com/intl/en/press/pressrel/20071008_ibm_univ.html [4]Apache Hadoop project: http://hadoop.apache.org [6]Jeffrey Dean, Sanjay Ghemawat: MapReduce: Simplified data processing on large clusters. In Proceedings of the 6th Conference on Symposium on Opearting Systems Design & Implementation, USENIX Association, Volume 6, pp. 10-10, December 2004. [12]High Performance Database Research Center (HPDRC), Research Division of the Florida International University, School of Computing and Information Sciences, University Park, Telephone: (305) 348-1706, FIU ECS-243, Miami, FL 33199. [16]Schnitzer B., Leutenegger S.T.: Master-client R-trees: a new parallel R-tree architecture, In Proceedings of the 11th International Conference on Scientific and Statistical Database Management, pp. 68-77, August 1999. [17]Apostolos Papadopoulos, Yannis Manolopoulos: Parallel bulk-loading of spatial data, Parallel Computing, Volume 29, Issue 10, pp. 1419 - 1444, October 2003. 22 Florida International University

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