Spatio-Temporal Histograms Hicham G. Elmongui* Mohamed F. Mokbel+ Walid G. Aref* *Purdue University, Department of Computer Science +University of Minnesota, Department of Computer Science elmongui@cs.purdue.edu, mokbel@cs.umn.edu, aref@cs.purdue.edu

Motivation Spatio-Temporal Database Server Infrastructure for keeping track and answering continuous queries on moving objects Moving Queries / Moving Objects Stationary Queries / Moving Objects Moving Queries / Stationary Objects Range Queries, KNN, … SSTD’05

Motivation Spatio-Temporal Database Server How many cars on this freeway? Stationary range query Moving data Where is my nearest McDonald’s? Moving KNN query Stationary data SSTD’05

Motivation SELECT M.ID FROM MovingObjects M WHERE M.Type = “Truck” INSIDE Area A; We cannot collect statistics statically (e.g. histograms) and answer queries efficiently over an extended period of time SSTD’05

Not just time makes a difference, but also space makes a difference Motivation Not just time makes a difference, but also space makes a difference Normalized Frequency Return home Go to work Lunch hour SSTD’05

Histograms aware of the underlying space and time dimensions ST-Histograms Histograms aware of the underlying space and time dimensions SSTD’05

System Architecture ST-Histogram Manager feedback Query Executor Data Plan Query Optimizer Continuous Query SSTD’05

Queries as Light Spots 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% SSTD’05

Queries as Light Spots 10% 6.98% 6.25% 6.25% 6.98% 6.25% 6.01% 6.01% SSTD’05

Queries as Light Spots 20% 6.98% 6.15% 6.98% 6.15% 6.01% 5.05% 6.01% 15.04% 6.01% Q2 6.01% 9.84% SSTD’05

Queries as Light Spots 6.15% 6.15% 5.05% 5.05% Q1 6.15% 6.15% 5.05% 15.04% Q2 15.04% 9.84% 9.84% SSTD’05

Queries as Light Spots 1% 6.15% 6.29% 6.29% 6.15% 5.21% 5.05% 5.21% 4.22% 5.05% 3.24% Q2 5.21% 5.05% 5.05% 5.21% 15.04% 15.51% 10.15% 9.84% SSTD’05

Features of ST-Histograms No computing capabilities assumed for the moving objects Moving objects update their location periodically with the spatio-temporal database server No patterns assumed for queries Queries come and go anytime anywhere Diskless spatio-temporal stream database server Enable for adaptive query processing SSTD’05

ST-Histogram Construction/Refining Initially Selectivity of a query Rate of a query to a grid cell SSTD’05

Experiments – Data Sets Network-based Generator of Moving Objects (SSDBM’00, GeoInformatica’02) Map of Greater Lafayette Area Every MO updates its location every 10 sec SSTD’05

Estimation Relative Error vs. Query Size SSTD’05

ST-Histogram’s Stability SSTD’05

ST-Histogram vs. Random Sampling SSTD’05

Related Work Spatio-temporal histograms Sampling Choi and Chung (SIGMOD’02) Tao et al (ICDE’03) Marios et al (SSDBM’03) Sampling Random Sampling Venn Sampling (ICDS’05) SSTD’05

Conclusion Aware of the underlying space and time dimensions Implemented in PLACE (a spatio-temporal database server) Efficient for spatio-temporal streaming applications Refined upon feedback from query executor Used in an online/offline mode Accommodate periodicity in moving objects’ behavior Enable adaptive query processing Average relative error 8% for practical query sizes SSTD’05

The END Thank You SSTD’05