Indexing the Past, Present, and Anticipated Future Positions of

Moving ObjectsMindaugas Pelanis, Simonas Saltenis, and Christian S. Jensen

http://portal.acm.org/citation.cfm?id=1132863.1132870

Kathy PhamCS 4440August 31, 2007

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!”

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):o Insurance risk manager considering location risk profileso Doctor comparing Magnetic Resonance Images (MRIs)o Emergency response determining quickest route to victimo Mobile phone companies tracking phone usage

Position of moving objects

• 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.

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

Record of Movement: 1-D

Linear prediction of future movement

Recorded polyline

u2

u3

u4 CT

xxx

time

Christian S. JensenTrajectory of 1-dimentional moving object

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.

Indexing Past separately from the Present

Left: To bridge gap, updates stored in near-past structure. Gap becomes arbitrarily large. Partially persistence index thatdisregards 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)

New Ideas

• Apply partial persistence (supports transaction time) to TPR-treeo For all time points the time-slice query performance should be asymptotically the same as the time-slice performance for the ephemeral structure.o 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

Types of TPBRs

• Straightforward TPBRsThe calculation of coordinates of bounding rectangles is modified:

the TPBR is computed to be minimum at its insertion time t├

• Optimized TPBRsMinimizes 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)

Straightforward TPBR

CT

The calculation of the coordinates of the bounding rectangles is modified: the TPBR is computed to be minimum at its insertion time t├.

CT

Time of last update

TPBR in TPR-tree

INSERTDELETE INSERT

TPBR in TPR-tree

Straightforward TPBR

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.

CT CT

INSERT

Time spilt

Dead entry Alive entry

Optimized TPBR

CT

INSERTDELETE INSERT

CT

Time spilt

Dead entry Alive entry

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.)

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.

Double TPBR: a head and a tail

”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.

CT

INSERTDELETE INSERT

CT

Double entryDouble entry

Double TPBR: a head and a tail

INSERT

Time spilt

Dead entry

Double TPBR: static headsinsert 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.

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)

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)

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

Thoughts?

kathy.pham@gatech.edu

Thanks to Christian S. Jensen for his notes.