1. Indexing the Past, Present, and Anticipated Future Positions of Moving Objects Mindaugas Pelanis, Simonas Saltenis, and Christian S. Jensen
Kathy Pham
CS 4440
August 31, 2007

2. Introduction: Me 5th Year Computer Science, graduating December!
Loved CS 4400
Wonder how the world operated before database systems
Initial interest in databases: mySQL and PHP
No background in database theory yet
Christian S. Jensen: “But, as you may have discovered, this is
fairly complex stuff to present... Good luck with the presentation!”

3. Introduction: Article
E-services to provide context-aware functionality to individual
users
Feasibility of storing all position information online
Efficient indexing techniques required
Current techniques index past or current/future positions
Proposed technique to capture position of moving objects at all
points in time by combining and extending past research.
Examples of users (from class):
Insurance risk manager considering location risk profiles
Doctor comparing Magnetic Resonance Images (MRIs)
Emergency response determining quickest route to victim
Mobile phone companies tracking phone usage
Current techniques capture position of object up most recent position sample. Others capture position of object as constant/linear function of time for present and future.
This article: all points
Massive amounts of data, disk resident
Great Disk capacities, slower advances in I/O

4. Position of moving objects
No index supports all three solid, solid-dashed, dashed parts
Two objects in 1-D space.
One index supports solid, other supports dashed.
Problem: no existing method indexes time between most
recent sample and current time.

5. Related Work: Past Position
Ephemeral data structures do not record history of changes
(B+ and R-trees were briefly discussed in class)
B+ trees: single dimensional indexes
R-tree: better than B+ trees, balanced on insert and delete
N-dimensional extension of B+ trees.
TB-tree
STR-tree
MV3R-tree: combined R-tree with partially persistent R-tree
can index past trajectory data
SETI: two-level indexign that separates spatial and
temporal
- This section is funny. They critique other groups.
- They cover all their bases! They discuss in detail all the other projects.

6. Record of Movement: 1-D x time Linear prediction of future movement
Recorded polyline u2 u3 u4 CT x
time
Each vertical line represents an update
Trajectory of 1-dimentional moving object
Christian S. Jensen

7. Related Work: Present and Future Position
Partially persistence data structures record history changes
PMR-Quadtrees
Time-Parameterized R-tree (TPR): Based of R*-tree,
index current/future, positions in 1-d, 2-d, 3-d
REXP-tree: extends TPR-tree to accommodate data with expiration
times
BBx-tree: past, present and future positions indexed,
but no trajectory segment corrections so
disconnected trajectories are indexed.
- This section is funny. They critique other groups.
They cover all their bases! They discuss in detail all the other projects.
Partially persistence: supports transaction time

8. Indexing Past separately from the Present
TPBR: time-parameterized bounding rectangle
Tightening: recomputing bounding rectangles each time tree node bounded by a rectangle is updated.
A rectangular bounding box is associated with each tree
node.
-Bounding box of a leaf node is a minimum sized rectangle that
contains all the rectangles/polygons associated with the leaf node.
-The bounding box associated with a non-leaf node contains the
bounding box associated with all its children.
-Bounding box of a node serves as its key in its parent node (if any)
-Bounding boxes of children of a node are allowed to overlap
Left: To bridge gap, updates stored in near-past structure.
Gap becomes arbitrarily large. Partially persistence index that
disregards present and future.
Right: Insertion times stored for all entries, no tightening possible,
both must be queried to get past queries (b/c of overlap)

9. New Ideas
Apply partial persistence (supports transaction time) to TPR-tree
For all time points the time-slice query performance should
be asymptotically the same as the time-slice performance
for the ephemeral structure.
The amount of space used by partial persistence index must
be proportional in terms of the number of updates.
Modify partial persistence to support valid time for monitoring
applications
TPR-tree produced TPBR cannot be used in RPPF-tree
New TPBR proposals
Partial persistence: supports transaction time

10. Types of TPBRs Straightforward TPBRs
The calculation of coordinates of bounding rectangles is modified: the TPBR is computed to be minimum at its insertion time t├
Optimized TPBRs
Minimizes the integral of the area of the bounding rectangle from t├ to CT+H (where H is a workload-specific parameter. Adjusted by observing the index workload)
Double TPBRs
“Head” bounds the segments of the trajectories of objects from t├ to the time of last update.
“Tail” starts at the time of last update, and it is the regular TPR-tree TPBR.
Two types of double TPBRs:
“heads” are optimized TPBRs
“heads” are static (zero speed)

11. Straightforward TPBR Time of last update TPBR in TPR-treeCT
TPBR in TPR-tree
TPBR in TPR-tree
INSERT
DELETE
INSERT CT
The calculation of the coordinates of the bounding rectangles is modified: the TPBR is computed to be minimum at its insertion time t├.

12. Straightforward TPBR Time spilt Alive entry Dead entry INSERT CT CT
Cons:
These TPBRs may result in bounding rectangles that grow fast and are not minimum at any point in time.
Not possible to do ”tightening”.
Bad bounding rectangles produced by the time split of bad alive bounding rectangles.

13. Optimized TPBR Time spilt Dead entry Alive entry INSERT DELETE INSERTCT CT
Minimizes the integral of the area of the bounding rectangle from t├ to CT+H.
(The workload-specific parameter H is adjusted by observing the worload.)

14. Optimized TPBR
Pros:
After the time split – possible to update the TPBR of the old node.
Cons:
Computation (using a convex hull) is complex and takes O(mn log n) time, where n is the number of objects bounded.
Not possible to do tightening.

15. Double TPBR: a head and a tail
Double entry
Double entry
INSERT
DELETE
INSERT CT CT
”Head” bounds the segments of the trajectories of objects from t├ to the time of last update. The optimized TPBRs are used.
”Tail” starts at the time of last update, and it is the regular TPBR.

16. Double TPBR: a head and a tail
Time spilt
Dead entry
INSERT

17. Double TPBR: static heads
insert I
insert II & time split
“Head” bounds the segments using the TPBR with static (zero speed) bounds.
Pros:
With respect to double optimized TPBRs, static TPBRs have the following advantages:
Reduces the size of the index entry
Omits the zero speeds in the double TPBR representation.
Computation is as simple as of MBRs in R-tree or TPBRs in TPR-tree.
Supports “tightening” (not possible in single optimized TPBRs).
Cons:
Heads may not be optimized. Might cover more space than double optimized TPBRs.
The time of the last update must be updated for all live ancestors at each update.
Update costs might be higher than using single optimized TPBRs.

18. RPFF-tree Use Double TPBRs with static heads
Performance comparison of the single and double optimized TPBRs:
I/O performance is similar, but the computation is much simpler.
TPBRs are rectangular (not trapezoids), therefore, less corrections of TPBRs will be done.
Indexes the past, present, and future positions of moving objects.
Past positions are captured as polylines.
Present and future positions are captured as linear functions.
Uses partial persistence
Uses novel kinds of time-parameterized bounding rectangles (TRBR)

19. Future Research
Apply partial persistence framework to other indexing techniques like Bx-trees
BBx trees can index past, present, future positions but trajectories from online updates have disconnected segments. Use this partial persistence and compare to Rppf tree.
Different methods of main memory use in Rppf trees.
Use this Rppf-tree for sensor data (like temperature, barometric pressure, humidity, etc)

20. Article Critique Strengths Short summaries inserted for clarification
Extensive research of previous ideas
Use of previous ideas
Build their case
Weaknesses
Tree discussion is confusing (when pro-ing and
when con-ing)
Figure labels not well defined

21. Thanks to Christian S. Jensen for his notes.
Thoughts?
Thanks to Christian S. Jensen for his notes.