Close Pair Queries in Moving Object Databases

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Close Pair Queries in Moving Object Databases
George Kollios Boston University

• Panfeng Zhou, Donghui Zhang, Betty Salzberg, Gene
  Cooperman
• Northeastern University

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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

3
Problem definition

• Example
• Which airplanes were closer to each other
  than 10 miles during the past month in
  Massachusetts?
• Formal definition
• Given a trajectory dataset D, a spatial range
  R, a time interval I and a threshold e, the
  Close-Pair Query finds all pairs of object IDs
  (o1, o2) such that at some time t ? I, o1 and o2
  are both located inside R and d(o1, o2) lt e.

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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Motivations

• Close pair query can be used to find associations
  and correlations between objects (e.g., S.
  Shekhar and Y. Huang, Discovering Spatial
  Co-location Patterns A Summary of Results, SSTD
  2001).
• Close pair query itself can be used in many real
  applications.

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Motivations (cont)
INCIDENTS
UNREPORTED OCCURRENCES
Heinrich Pyramid
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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Algorithm

• Overview Structure
• Retrieval component
• Identification component

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Overview structure of algorithm
Close pairs
Trajectories in increasing time order
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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Retrieval component

• Overview of the MTSB-tree
• Challenges in the MTSB-tree
• How to avoid sorting
• How to avoid duplication

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Overview of the MTSB-tree

• Note
• Trajectory covers multi- cells will be saved in
  all those cells.
• The retrieval algorithm will first find all the
  cells intersect spatial range R. Within each
  cell, load all the pages intersect time range I.

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Challenges in the MTSB-tree

• Output the retrieval results in time increasing
  order.
• Avoid loading the same trajectory multiple times.

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How to avoid sorting - 1
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
Cell 1
Cell 2
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid sorting - 2
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
T1, L11
Cell 1
Cell 2
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid sorting - 3
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
T1, L11
Cell 1
Cell 2
T2, L21
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid sorting - 4
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
T1, L12
Cell 1
Cell 2
T2, L21
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid sorting - 5
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
T2, L21
Cell 1
Cell 2
T5, L13
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid sorting - 6
Page 1
Page 2
Priority Queue
T1, L12
T7, L14
T1, L11
T5, L13
Cell 1
T4, L22
Cell 1
Cell 2
T5, L13
Page 1
Page 2
T4, L22
T8, L24
T2, L21
T6, L23
Cell 2
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How to avoid duplication loading from different
cells
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How to avoid duplication loading from the same
cell
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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Identification component

• Motivation for TIME-X sweep algorithm
• Observations
• Algorithm

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Motivation
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Observations

• Only need to detect close pairs at start times,
  end times and intersections

• If two trajectory segments do not intersect,
• they are closest at the start/end time of one of
  them

• Store trajectories relative positions in
  X-dimension at their start times and update the
  order at intersections, we can always keep the
  correct relative order

• If two trajectory segments do not intersect,
• their relative positions will never change

• If two trajectory segments distance at
  X-dimension
• is bigger than e, their distance at X-Y plane is
  also
• bigger than e

• Plane sweep at TIME-X plane can filter out the
  unqualified close pair candidates in TIME-X-Y
  plane.

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Algorithm - 1
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Algorithm - 2
X
L1
t1
t8
Time
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Algorithm - 3
X
L2
L1
t1
t3
t8
t12
Time
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Algorithm - 4
X
L2
L3
L1
t1
t3
t5
t8
t11
t12
Time
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Algorithm - 5
X
L2
L3
L4
t3
t5
t7
t10
t11
t12
Time
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Algorithm - 6
X
L2
L3
t3
t5
t11
t12
Time
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Algorithm - 7
X
L2
t3
t12
Time
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Algorithm - 8
X
Time
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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Experimental results

• Setup
• Retrieval component
• Identification component

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Setup

• Simulated Air Traffic Control data set includes
  200,000 3-D line segments and the whole space is
  a 10000x10000x10 space.
• 4D R-tree (i.e., 3D for spatial, 1D for
  temporal) uses the XXL library
• Page size 16KB

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Retrieval component - 1
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Retrieval component - 2
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Identification component
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Talk Outline

• Problem description
• Motivation
• Algorithm
• Overview structure
• Retrieval component
• Identification component
• Experimental results
• Conclusions

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Conclusions

• The MTSB-tree can efficiently return the
  retrieval results without sorting.
• The Time-X plane sweep algorithm can avoid the
  unnecessary comparisons.
• The efficiency of the methods are verified by
  extensive experimental results.

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Thank you!