1 spatial-temporal database and moving objects management
TRANSCRIPT
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Spatial-temporal Database and moving objects management
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Outlines
Introduction Background knowledge Spatial database Spatial-temporal database Moving objects management Conclusions
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Introduction
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Introduction Location-aware database services
GPS technology GIS system Vehicular database Wireless communication technology
Location update
Location update
Query
Query
Answer
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Introduction
Location-based applications Traffic monitoring and management Location-based store (services) find and advertisement People cooperation and communication
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Various Queries
How many cars in this area?
Static Query over moving Object
Location-aware Database Server
Keep talking with 3 nearest police cars
Moving Query over moving Object Continuous K-nearest Neigbor
How many cars in Highlight now?
Moving Query over moving Object Snapshot
Moving Query over Static Object
Keep me updated by hospitals in 3 miles
Keep updating how many airplanes within
100 miles
Moving Query over moving Object Continuous Range Based
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Target Query Moving Continual Queries over moving object
(MCQ)
Generalization of Moving and Static Queries
Continuous nature1 continuous query = a sequence of snapshot queries with some frequency
Range-based or kNN
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Background knowledge
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History of Database Technology
1960s: Data collection, database creation, IMS and network DBMS
1970s: Relational data model, relational DBMS implementation
1980s: RDBMS, advanced data models (extended-relational, OO, deductive, etc.) and application-oriented DBMS (spatial, scientific, engineering, etc.)
1990s—2000s: Data mining and data warehousing, multimedia databases, and Web databases
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Structure of a RDBMS
A DBMS is an OS for data!
A typical RDBMS has a layered architecture.
Query Optimizationand Execution
Relational Operators
Files and Access Methods
Buffer Management
Disk Space Management
DB
Modern Database SystemsExtend these layers
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Index Methods for RDBMS
Hashing Methods
B-tree family
Both of them are one-dimensional
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B+-tree
Records must be ordered over an attribute
Queries exact match or range queries over the indexed
attribute find the name of the student with SID=dr868301 find all students with gpa between 3.00 and 3.5
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B+-tree:properties
“B” for balance! Each node contains up to n-1 search key
values and n pointers A nonleaf node may hold up to n pointers
and must hold at least Two types of nodes: index nodes and data
nodes; each node is 1 page (disk based method)
2/n
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57
81
95
to keys to keys to keys to keys
< 57 57 k<81 81k<95 95
Index node
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Data node5
7
81
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To r
eco
rd
wit
h k
ey 5
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To r
eco
rd
wit
h k
ey 8
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To r
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rd
wit
h k
ey 8
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From non-leaf node
to next leaf
in sequence
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EX: B+ Tree of order 3.
(a) Initial tree
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80
20 , 40
205,10 6040,50 80,100
Index level
Data level
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Query Example
Root
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3 5 11
30
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100
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180
200
Range[32, 160]
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Insertion Find correct leaf L. Put data entry onto L.
If L has enough space, done! Else, must split L (into L and a new node L2)
Redistribute entries evenly, copy up middle key. Insert index entry pointing to L2 into parent of L.
This can happen recursively To split index node, redistribute entries evenly, but push
up middle key. (Contrast with leaf splits.) Splits “grow” tree; root split increases height.
Tree growth: gets wider or one level taller at top.
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Deletion
Start at root, find leaf L where entry belongs. Remove the entry.
If L is at least half-full, done! If L has only d-1 entries,
Try to re-distribute, borrowing from sibling (adjacent node with same parent as L).
If re-distribution fails, merge L and sibling. If merge occurred, must delete entry (pointing to L or
sibling) from parent of L. Merge could propagate to root, decreasing height.
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Create a B+ tree Insertion order: 9, 6, 1, 8, 4, 13
6, 9
1
6
6, 9
1
6 , 8
6 8, 9
1, 4
6 , 8
6 8, 9
8
61, 4
9,138
6 9
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Insert a key
Insert a key into a leaf which still has some room (not overflow).
Put the keys of this leaf in order.
No changes are made in the index level.
1
6
6, 9
1, 4
6
6, 9
insert 4
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If a key is inserted into a full leaf (overflow) Split, the new leaf node is included in the sequence
set, keys are distributed evenly between the old and the new leaves, and the first key from the new node is copied (not moved, as in B-tree)
1, 4
6
6, 9
1, 4
6, 9
6
The parent is not full The parent is full
Insert 10
9,10
Insert 3
1
3
6 9,103, 4
6
6, 9
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Delete a key Delete a key from a leaf leading to no underflow Delete the leaf and keep remaining keys in
order index level !
delete 4
1, 4
6, 9
6 9,10 1
6, 9
6 9,10
delete 9
1, 4
6, 10
6 10 1, 4
6, 9
6 10
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Spatial database
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Introduction
A common technology for some Applications: GIS (geographic/geo-referenced data) VLSI design (geometric data) modeling complex phenomena (spatial data)
All need to manage large collections of relatively simple spatial objects
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SDBMS DefinitionA spatial database system: Is a database system
A DBMS with additional capabilities for handling spatial data
Offers spatial data types (SDTs) in its data model and query language Structure in space: e.g., POINT, LINE, REGION Relationships among them: (l intersects r)
Supports SDT in its implementation providing at least spatial indexing (retrieving objects in particular area
without scanning the whole space) efficient algorithms for spatial joins (not simply filtering
the cartesian product)
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Modeling
Assume 2-D and GIS application, two basic things need to be represented:
Objects in space: cities, forests, or rivers single objects
Coverage/Field: say something about every point in space (e.g., partitions, thematic maps)
spatially related collections of objects
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Modeling: spatial primitives for objects
Point: object represented only by its location in space, e.g. center of a state
Line (actually a curve or ployline): representation of moving through or connections in space, e.g. road, river
Region: representation of an extent in 2d-space, e.g. lake, city
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Modeling: spatial relationships
Topological relationships: e.g. adjacent, inside, disjoint. Are invariant under topological transformations
like translation, scaling, rotation
Direction relationships: e.g. above, below, or north_of, sothwest_of, …
Metric relationships: e.g. distance
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Spatial Queries
Given a collection of geometric objects (points, lines, polygons, ...)
organize them on disk, to answer efficiently point queries range queries k-nn queries
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Spatial Queries
Given a collection of geometric objects (points, lines, polygons, ...)
organize them on disk, to answer point queries range queries k-nn queries
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Spatial Queries
Given a collection of geometric objects (points, lines, polygons, ...)
organize them on disk, to answer point queries range queries k-nn queries
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Spatial Queries
Given a collection of geometric objects (points, lines, polygons, ...)
organize them on disk, to answer point queries range queries k-nn queries
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Access Methods
Discussed in the course Grid file K-d tree Z curve R-tree
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The problem
Given a point set and a rectangular query, find the points enclosed in the query (range)
Given a point set and a point query q, find the point nearest to q (NN,KNN)
Query
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Grid File
Idea: Use a grid to partition the space each cell is associated with one page
Two disk access principle
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Grid File
Start with one bucket for the whole space.
Select dividers along each dimension. Partition space into cells
Dividers cut all the way.
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Grid File
Each cell corresponds to 1 disk page.
Many cells can point to the same page.
Cell directory potentially exponential in the number of dimensions
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Grid File Implementation
Dynamic structure using a grid directory Grid array: a 2 dimensional array with pointers to
buckets (this array can be large, disk resident) G(0,…, nx-1, 0, …, ny-1)
Linear scales: Two 1 dimensional arrays that used to access the grid array (main memory) X(0, …, nx-1), Y(0, …, ny-1)
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Example
Linear scale X
Linear scale
Y
Grid Directory
Buckets/Disk
Blocks
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Grid File Search Exact Match Search: at most 2 I/Os assuming linear scales fit in
memory. First use liner scales to determine the index into the cell
directory access the cell directory to retrieve the bucket address (may
cause 1 I/O if cell directory does not fit in memory) access the appropriate bucket (1 I/O)
Range Queries: use linear scales to determine the index into the cell directory. Access the cell directory to retrieve the bucket addresses of
buckets to visit. Access the buckets.
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K-d tree K-d tree is a main memory binary tree for
indexing k-dimensional points
The kd-tree is a data structure that is based on recursively subdividing a set of points with alternating axis-aligned hyperplanes.
K-d tree is not necessarily balanced
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Kd-trees
l1
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Kd-trees. Construction
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Z-ordering
Map points from 2-dimensions to 1-dimension. Use a B+-tree to index the 1-dimensional points
Basic assumption: Finite precision in the representation of each co-ordinate, K bits (2K values)
The address space is a square (image) and represented as a 2K x 2K array
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Z-ordering
Impose a linear ordering on the pixels of the image 1 dimensional problem
00 01 10 1100
01
10
11
A
B
ZA = shuffle(xA, yA) = shuffle(“01”, “11”)
= 0111 = (7)10
ZB = shuffle(“01”, “01”) = 0011
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Z-ordering
Given a point (x, y) and the precision K find the pixel for the point and then compute the z-value
Given a set of points, use a B+-tree to index the z-values
A range (rectangular) query in 2-d is mapped to a set of ranges in 1-d
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Queries
Find the z-values that contained in the query and then the ranges
00 01 10 1100
01
10
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QA range [4, 7]QA
QB
QB ranges [2,3] and [8,9]
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R-trees
[Guttman 84] Main idea: allow parents to overlap! => guaranteed 50% utilization => easier insertion/split algorithms. (only deal with Minimum Bounding Rectangles -
MBRs)
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R-trees
A multi-way external memory tree Index nodes and data (leaf) nodes All leaf nodes appear on the same level Every node contains between m and M entries The root node has at least 2 entries (children)
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R-Tree
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R-Tree
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Range query: find the objects in a given range.E.g. find all hotels in Boston.
No index: scan through all objects. Inefficient!B+-tree: only cluster based on one dim. Inefficient!
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R-Tree: Clustering by Proximity
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Minimum Bounding Rectangle (MBR)
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R-Tree
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R-Tree
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R-Tree
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R-tree properties
a b c d e
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Root
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E5
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disk-based: stored on disk, load to memory the needed part. balanced: all leaf nodes have the same distance from root. dynamically-updateable: dynamic insertion/deletion leaf-storage: all records are stored in leaf nodes. min-capacity: every node (except the root) is at least half full.
R-Tree structure leaf entry = <object>
index entry = <MBR, ptr to child node> MBR of all objects in the subtree.
Observation: if Q does not intersect an MBR, no object in the sub-tree is inside Q.
QMBR
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MBR face property
MBR is a d-dimensional rectangle, which is the minimal rectangle that fully encloses (bounds) an object (or a set of objects)
MBR f.p.: Every face of the MBR contains at least one point of some object in the database
Range query (given range Q)
Start at root.1. If current node is non-leaf, for each entry <E, ptr>, if box E overlaps Q, search subtree identified by ptr.2. If current node is leaf, for every object in the leaf page, report if contained in Q.
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Range Query
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Range Query
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KNN Search in a R tree
Visit an MBR (node) only when necessary
How to do pruning? Using MINDIST and MINMAXDIST
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MINDIST
MINDIST(P, R) is the minimum distance between a point P and a rectangle R
If the point is inside R, then MINDIST=0 If P is outside of R, MINDIST is the distance of P to the closest
point of R (one point of the perimeter)
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MINDIST computation
MINDIST(p,R) is the minimum distance between p and R with corner points l and u the closest point in R is at least this distance away
ri = li if pi < li
= ui if pi > ui
= pi otherwise
pp
p
R
l
u
MINDIST = 0
d
iii rpRPMINDIST
1
2)(),(
l=(l1, l2, …, ld)
u=(u1, u2, …, ud)
),(),(, oPRPMINDISTRo
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MINDIST and MINMAXDIST
MINDIST(P, R) <= NN(P) <=MINMAXDIST(P,R)
R1
R2
R3 R4
MINDIST
MINMAXDIST
MINDISTMINMAXDIST
MINMAXDIST
MINDIST
Insert object o Start at root and go down to “best-fit” leaf L.
Go to child whose box needs least enlargement to cover B; resolve ties by going to smallest area child.
If best-fit leaf L has space, insert entry and stop. Otherwise, split L into L1 and L2. Adjust entry for L in its parent so that the box now
covers (only) L1. Add an entry (in the parent node of L) for L2. (This
could cause the parent node to recursively split.)
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E.g. 1: no split, no enlargement
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insert o
o
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E.g. 2: no split, but enlargement
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insert o
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E.g. 2: no split, but enlargement
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E.g. 3: split
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E.g. 3: split
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R-trees: Variations
R+-tree: DO not allow overlapping, so split the objects (similar to z-values)
R*-tree: change the insertion, deletion algorithms (minimize not only area but also perimeter, forced re-insertion )
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Spatio-Temporal Databases
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Introduction
Spatio-temporal Databases: manage spatial data whose geometry changes over time
Geometry: position and/or extent Global change data: climate or land cover changes Transportation: cars, airplanes Animated movies/video DBs
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ST DBs
A special Temporal Database All the features of temporal database Attributes can be spatial also
Extension of Spatial Databases Objects change instead of being static At any timestamp it is a conventional Spatial
Database New Database type
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Requirements
Efficient Representation of Space and Time Data Models Query Languages Query processing and Indexing GUI for spatio-temporal datasets
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Spatio-temporal Objects
(a) (b) a moving point a moving and shrinking region
y
t
x
y
t
x
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ST Queries
Range Queries: “find all objects contained in a given area Q at a given time t”
NN queries: “find which object became the closest to a given point s during time interval T,”
Aggregate queries: “find how many objects passed through area Q during time interval T,” or, “find the fastest object that will pass through area Q in the next 5 minutes from now”
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ST Queries
join queries: “given two spatiotemporal relations R1 and R2, find pairs of objects whose extents intersected during the time interval T,” or “find pairs of planes that will come closer than 1 mile in the next 5 minutes”
similarity queries: “find objects that moved similarly to the movement of a given object o over an interval T”
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SP Data Types
Moving Points Extent does not matter Each object is modeled as a point (moving vehicles in a
GIS based transportation system) Moving regions
Extent matters! Each object is represented by an MBR, the MBR can
change as the object move (airplanes, storm,…)
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SP Data Types
Different Type of changes: Changes are applied discretely
Urban planning: appearance or dis-appearance of buildings
Changes are applied continuously Moving objects (eg. Vehicles)
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Trajectories
Moving objects create trajectories Usually we can sample the positions of the objects at
periodic time intervals t Linear Interpolation:easy and usually accurate enough Trajectory: a sequence of 2 or 3-dim locations
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Temporal Environment
Valid time Two types of environments:
Predicting the future positions: Each object has a velocity vector. The DB can predict the location at any time t>tnow assuming linear movement. Queries refer to the future
Storing the history. Queries refer to the past states of the spatial database
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The Historical Environment
Spatio-temporal Evolution
x x x x x
t
t1 t5t4t3t2
S(t1) S(t5)S(t4)S(t3)S(t2)
y y y y y
o2 o2o2 o2
o3 o3 o3o3
o1o1 o1
o1o1
Queryregion Q
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Indexing using R-trees
Assume that time is another dimension, use a 3D R-tree Store the objects as their 3D MBR. How to compute that?
x
tt1
t3t2
y
o2
o3
Query region Q
o1
t4 tnow
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Problems of 3D R-tree
How to store “now”? Use a large value… Long lived objects will have very long MBRs, difficult to cluster Extensive overlap and empty space bad query performance
for specific queries Also, works only for discrete changes
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Indexing Moving Objects
The problem of indexing any type of moving objects can be reduced to indexing discrete rectangles.
Continuous points Continuous rectanglesDiscrete rectangles
xy
time
t
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Historical R-trees (HR-trees)
o1
o2
o6
o7
o5
p1 p2 p3
o1 o2 o3 o4 o5 o6 o7
p1
p2
p3
o4o3
timestamp 1
timestamp 1
An R-tree is maintained for each timestamp in history.
Trees at consecutive timestamps may share branches to save space.
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Historical R-treesAn R-tree is maintained for each timestamp in history.
Trees at consecutive timestamps may share branches to save space.
p1 p2 p3
o1 o2 o3 o4 o5 o6 o7
timestamp 1 p1 p2’ p3’
o3 o4
timestamp 2
o3 o4 o5’
o1
o2
o6
o7
o5’
p1
p2’
p3’
o4o3 timestamp 2
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HR-trees: Pros and Cons
• HR-trees answer timestamp queries very efficiently.
– A timestamp query degenerates into a spatial window query handled by the corresponding R-tree at the query timestamp.
• Not quite efficient:
– Expensive space consumption.
A node needs to be duplicated even when only one object moves.
– Interval query processing is inefficient.
Although redundancy (from duplication) is necessary to maintain good timestamp query performance, it is excessive in HR-trees.