AAU

Novel Approaches to the Indexing of Moving

Object Trajectories

Presented by YuQing Zhang

Dieter Pfoser Christian S. Jensen Yannis Theodoridis

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Contents Introduction1

Moving Objects2

Access Methods3

Query Processing4

Performance Comparison5

Conclusion and Future Works6

Strength and Weakness7

Relate to My Project8

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Introduction

Objects in Real World Space Time

Preservation of trajectories Line segments belong to the same trajectory With respect to time

Access Methods

Spatio-Temporal R-Tree (STR-tree)

Methods

Trajectory-Bundle Tree (TB-tree)

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Moving Object

Trajectories How to represent the movements of objects

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Simply Store the position samples

2

Linear Interpolation

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Moving Objects

Trajectories Spatiotemporal Workspace Temporal Dimension

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Moving Objects

Queries Coordinate-based Queries: point, range and nearest neighbor

Example: Find all buses within AAU during 8.00AM - 9.00PM

Trajectory-based Queries Topological Queries : important but expensive

Example: Whether the BUS 17 entered AAU at 8.00AM Navigation Queries: speed or heading

Example: What is Bus 17’s top speed?

Combined Queries Example: What were the trajectories of buses after they left AAU between 7am-8am today in the

next hour?

Querying trajectory identifier

Selecting a segment

Using a topological query

Using derived information

Select the trajectories

Select the parts of each trajectory

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Access Methods --- R tree

What is R-tree Height balanced tree Index records in leaf nodes Pointer to actual data

Inefficiencies of R-tree Dead Space Hard to determine a line segment belongs to

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Access Methods --- STR-tree Difference with R-tree

Insertion/split Strategy

Insertion Strategy Not only spatial closeness, but also trajectory preservation R-tree: least enlargement criterion STR-tree: keep line segments belong to the same trajectory

Insertion Algorithm FindNode() Preservation parameter

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Access Methods --- STR-tree

Spilt Strategy General idea: put newer and thus more recent segments into new nodes A node can contain:

1Disconnect

ed segments

2Forward

(backward)Connected segments

3Bi-

connected segments

aa Quadratic Spilt Algorithm bbThe disconnected segments are placed into the newly created node.

ccThe most recent backward-connected segment is placed into the newly created node.

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Access Methods --- TB-tree

Take a radical step

Concession: node overlap or spatial discrimination

R-tree

STR-tree

line segments are parts of trajectories and this knowledge is only implicitly maintained

TB-tree

strictly preserves trajectories such that a leaf node only contains segments belonging to the same trajectory

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Access Methods --- TB-tree

Insertion Algorithm

Goal: cut the whole trajectory of a moving object into pieces

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Access Methods --- TB-tree

Trajectory Preservation A double linked List: preserves trajectory evolution

simple solution to retrieve segments based on trajectory identifier

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Query Processing

Combined Search in the R-tree and STR-tree retrieve an initial set of segments based on a spatiotemporal range extract partial trajectories not retrieving the same trajectory twice

3 4

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Query Processing

Combined Search in the TB-tree the difference lies in how the partial trajectories are retrieved

the linked list allow us to retrieve connected segments without searching

two possibilities: a connected segment can be in the same leaf node or in another node

Same: finding it is trivial Another: follow the pointer

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Performance comparison

Datasets GSTD generator

Space Utilization and Index Size Space Utilization: R-tree is the smallest Index size: R-tree is the biggest

TB-tree is smaller than that of STR-tree

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Performance comparison

Summary

Time slice Queries

Trajectory-based Queries

Combined Queries

R-tree

STR-tree √

TB-tree √ Number of MO

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Conclusion and Future Work

Conclusion presents a set of pure spatiotemporal queries trajectory-based queries combined queries

Shortcomings of R-tree

STR-tree TB-tree STR-tree performance stays behind the TB-tree

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Conclusion and Future Work

Future Work

Refine navigational and topological queries more detail. Pay attention to some expensive spatial queries. Investigating geometric shapes other than MBBs as approximations for

moving objects’ trajectories deserves further research

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Relate to my Project

My project Range queries

Use Oracle

Maybe… Give another view of questions

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Strength and weakness

Strength

Describe each method quite clearly Use some comparison Some figures are helpful

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Strong and weakness

Weakness

No Related Work introduction Some parameters in some algorithms are ambiguous Reader must have the knowledge of R-tree

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Questions?

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Presented by YuQing Zhang