Continuous Intersection Joins
Over Moving Objects
Rui Zhang
University of Melbourne
Dan Lin
Purdue University
Kotagiri Ramamohanarao
University of Melbourne
Elisa Bertino
Purdue University
Outline

Backgrounds



Intersection Joins on moving objects
Indexes for moving objects
Algorithms


Adapting existing algorithms
Our approach
 Time constrained processing


Improvement techniques
Experiments
Motivation

(Traditional) Intersection join


Given two sets of spatial objects A and B, find all object
pairs ‹i,j›, where iA, j B, such that i intersects j.
Intersection join on moving objects


Moving
Continuous
Join Algorithms

Nested loops join



Block nested loops join



Efficient
Dependent on buffer size
Index nested loops join


Basic
Expensive
Efficient and robust
Sort-merge join


Efficient
Difficult for spatial objects
u
Indexing Moving Objects



Minimum bounding
rectangle (MBR)
TPR-tree [SIGMOD’00]

Add time parameters to the
R-tree
Other indexes: Bx-tree
[VLDB’04], STRIPES
[SIGMOD’04]

u
p = p ( t ref ) + v (t - t ref )
TM : maximum update
interval
Only for points
u
u
R-tree [SIGMOD’84]


u
Sampling-based
Trajectory-based


u
Monitoring moving objects


u
N31
N3
A N1
C
N1 N2
D
N1
F
A C D
E N2 B
N2
B E F
Naive Algorithm (NaiveJoin)

Join nodes from two TPR-trees recursively



If intersected, check on children
Otherwise, disregard it
For an update, compute its join pairs and update the answer
Join result
‹a1,b1›, [0,3]
‹a2,b2›, [1,4]
‹a3,b4›, [6,8]
Node access (IO)
roots, N1, N2, N3,
N4
Comparison (CPU)
root A vs root B, N1
vs N3, N2 vs N4
Extended TP-Join Algorithm (ETP-Join)

Time Parameterized Join (TP-Join) [SIGMOD’02]



Current result ‹a1,b1›
Expiry time 1
Event that causes the change ‹a2,b2›
Join result
‹a1,b1›, [0,3]
‹a2,b2›, [1,4]
‹a3,b4›, [6,8]
For the 1st TP-Join
Node access (IO)
roots, N1, N3
Comparison (CPU)
root A vs root B, N1
vs N3
Summary

NaiveJoin

One tree traversal per
update, but expensive
traversal

ETP-Join

Cheaper traversal, but
too frequent traversals
For the 1st TP-Join
Node access (IO)
Node access (IO)
roots, N1, N2, N3,
N4
roots, N1, N3
Comparison (CPU)
Comparison (CPU)
root A vs root B, N1
vs N3, N2 vs N4
root A vs root B, N1
vs N3
Too long
Too short
Key Problem

Find a good time range for computing the join pairs

Observation




How do we know ta or tb?



Consider object a and b
Let the next update time for them be ta and tb
Perfect time range for computing their join result is [tc, min(ta,tb)]
TM gives a bound for them
Time range is cut from [tc, ] to [tc, tc+TM]
Is this correct for all objects?

Yes. Proof in technical report:
http://www.cs.mu.oz.au/~rui/publication/TR_mj.pdf
Time Constrained Processing (TC-Join)

NaiveJoin with constrained processing time
range [tc, tc+TM]
Join result
‹a1,b1›, [0,3]
‹a2,b2›, [1,4]
‹a3,b4›, [6,8]
Node access (IO)
roots, N1, N3
Comparison (CPU)
root A vs root B, N1
vs N3
Further Optimization (MTB-Join)

Many objects will not update at the time bound

Put objects in time buckets


Each time bucket has an associated TPR-tree
An object is inserted into the tree whose time
bucket contains the object’s latest update time
tc is in [TM, 3/2TM]
Improvement on the Basic Join Algorithm

Plane Sweep



Sorting based on the lower left corner in dimension x
Two sequences: Sa = ‹a3, a4, a5›; Sb = ‹ b1, b2, b3, b4›
Two essential components for PS


Lower bound
Upper bound
Other Improvements

Sorting dimension selection


Smaller average speed
Intersection check

First intersection check and then plane sweep
Experiments: setting

Computer: 2.6G Pentium IV CPU, 1G RAM

Datasets: Uniform, Gaussian, Battlefield

Measure: IO and Time
Parameter
Value
Node capacity
113
Maximum update interval (TM)
60, 120, 240
Maximum object speed
1, 2, 3, 4, 5
Object size (% of space)
0.5, 0.1, 0.2, 0.4, 0.8
Dataset size
1K, 10K, 50K, 100K
Dataset
Uniform, Gaussian, Battlefield
Experiments: TC processing
Up to 15 times improvement
Experiments: Improvement techniques
Up to 6 times improvement
Comparison: Initial Join
MTB-Join outperforms others
Half an hour for NaiveJoin
Comparison: Maintenance
Up to 104 times improvement
Time for processing the join for one second
1K
10K
100K
MTB-Join
0.03 millisecs
0.05 secs
6 secs
ETP-Join
6.3 secs
15 mins
hours
Conclusion and future work


Conclusion

Time Constrained processing

Further optimization by bucketing in time

Improvement techniques

Several orders of magnitude performance
improvement
Future work

Applying TC processing to other queries
References

R-tree [SIGMOD’04]


TPR-tree [SIGMOD’00]


C. Jensen, D. Lin, and B.C.Ooi. Query and update efficient B+-tree based
indexing of moving objects. International conference on Very Large
Databases, 2004.
STRIPES [SIGMOD’04]


S. Saltenis, C. S.Jensen, S. T. Leutenegger, and M. A. Lopez. Indexing the
positions of continuously moving objects. ACM SIGMOD Conference
2000.
Bx-tree [VLDB’04]


Antonin Guttman. R-Trees: A Dynamic Index Structure for Spatial
Searching . ACM SIGMOD Conference 1984.
J. M. Patel, Y. Chen, and V. P. Chakka. STRIPES: An efficient index for
predicted trajectories. ACM SIGMOD Conference 2004.
TP-Join [SIGMOD’02]

Y. Tao and D. Papadias. Time-parameterized queries in spatio-temporal
databases. ACM SIGMOD Conference 2002.
Questions
Please send your questions to
Rui Zhang
rui@csse.unimelb.edu.au