15-823 Questions Advanced Topics in Database Systems Performance
What is spatial data ?

How to represent spatial data?

Spatial Application
What are the queries?

How to process the query? Ti ankai Tu Computer Science Department [email protected] mu.edu

Spatial Application 2

Spatial Data:Definition Spatial Data:Features

Data that pertains to the space occupied
Geometric and varied by objects
Naturally high dimensional
Conceptually, points, lines, rectangles,
Can be either discrete or continuous surfaces, volumes and etc.
May associate with non-spatial attributes
Physically, cities, rivers, roads, states, crop coverage, mountain ranges etc.
Applications include environmental monitoring, geographic information systems, earthquake research etc.

Spatial Application 3 Spatial Application 4

Spatial Data and DBMS A Motivating Example

How: turn spatial data into tuples
Pittsburgh road database
Termed representative point
Suppose the roads are straight lines (forget about Forbes for this example)
Parameterized representation
A representative point consists of two endpoints, that
Non-spatial attributes stored together is, a tuple of four four items
It works for simple retrieval and queries
Mapping from a two-dimensional (drawing)spacetoa four-dimensional (transformed) space
Why not: unnatural
Queries
Dimension of representative point too high
What are the roads originating from Point State Park?
Deducing dimensionality lose important
Which road is the closest to Wean Hall? physical information such as proximity
Which roads go through CMU?
Clumsy for queries involving space

Spatial Application 5 Spatial Application 6

1 Spatial Data Representation Spatial Indexing

Follow the natural way: spatial occupancy
All the spatial occupancy methods are
Decompose the space from which the data characterized as employing spatial is drawn into buckets indexing
Four principal approaches
Each block/cell/rectangle only contains
Minimum bounding rectangles: data-dependent information about whether or not it’s
e.g. R-tree [Guttman 1984], R* -tree [Beckmann et al. 1990]
Disjoint cells: data-dependent occupied by the object or part of the object +
e.g. R -tree [Sellis et al. 1987], Cell tree [Günther 1988]
The information is usually in the form of a
Uniform size blocks: data-independent
e.g. Uniform grid [Franklin 1984] pointer to a descriptor of the object
Adaptive regular blocks: data-independent
e.g. Quadtree-based approach [Same et al. 1985]

Spatial Application 7 Spatial Application 8

Spatial Indexing (cont.) Case Study:R-Tree

The shaded block only
Goal: efficient retrieval of objects records the fact line according to their spatial location b segment c crosses it a
h e
The part of the line that Conventional DBMS indexing structure g passes through or
i Hashing: cannot handle range query f terminates in a block is d termed q-edge
B-tree: cannot handle multi-dimensional data c
Each q-edge in the block is
Key ideas: represented by a pointer to a record containing the end
Maintain balanced hierarchical tree structure Example collection of line segments embedded in a 4x4 grid points of the line segment
Represent objects by intervals in several
No information about what dimensions part the line crosses it
Take care of secondary memory paging

Spatial Application 9 Spatial Application 10

R-Tree:Example R-Tree:Example (cont.)

R1 R1 b R3 b R3 b R1 R2 a R2 a R6 R2 a R6 h e h e h e g g g i i i R3 R4 R5 R6 f f f d d d c R4 c R4 c R5 R5 a b d g h c i e f

Example collection of line segments Spatial extents of the bounding Spatial extents of the bounding R-tree representation of line segments embedded in a 4x4 grid rectangles for R-tree rectangles for R-tree

Spatial Application 11 Spatial Application 12

2 R-Tree:Properties R-Tree:Properties (cont.)

Height-balanced tree similar to B-tree
Every node contains between m and M
All leaves appear on the same level entries unless it is the root
Leaf nodes contain index record entries of
M : maximum number of entries that fit in one node. the form (I,tuple-identifier)
m: minimum number of entries in a node (m ≤ M/2)
Nodes correspond to disk pages
tuple-identifier: a tuple in database
I:an n-dimensional rectangle that bounds the spatial
Root node has at least two children unless object indexed it is a leaf
Non-leaf nodes contain entries of the form (I,child-pointers)
child-pointer: the address of a lower node in the R-tree
I : bounds all rectangles in the lower node’sentries

Spatial Application 13 Spatial Application 14

R-Tree:Search R-Tree:Search (cont.)

Search Algorithm
Acclaimed strength R1
Eliminate irrelevant regions
Given an R-tree rooted at T, find all records R3 b of the indexed space and whose rectangles overlap search rectangle S R2 a R6 h e examine only data near the g
Denote the rectangle part of an index entry E by EI, search area, thus visit only a i and the tuple-identifier or child-pointers by Ep f small number of nodes d
Search subtree:IfT is not a leaf, check each entry E Q R4 c
Criticized drawback: to determine whether EI overlaps S; For all R5 overlapping entries, invoke Search subtree on the
More than one subtree under tree rooted at Ep a node may be searched, Spatial extents of the bounding thus potential search the
Search leaf node:IfT is a leaf, check all entries E to rectangles for R-tree entire spatial database determine whether EI overlaps S.Ifso,E is a qualifying record
Bad example:find the line segment passing through Q

Spatial Application 15 Spatial Application 16

R-Tree:Insert R-Tree:Insert (cont.)

Similar to insertion in B-tree
How to choose leaf node
New index records are added to the
Descend the tree leaves, nodes overflow are split, and split
At each non-leaf node, choose the entry that propagate up the tree needs least enlargement to include the new index entry; follow the child-pointer link of this
Key issues: entry to find next level non-leaf node
Choose leaf node for the first insertion
How to adjust parent nodes
Adjust nodes as changes propagate up
Enlarge I of the entry in the parent node still
Split node if it becomes too full ( > M ) tightly encloses all entry rectangles in child node

Spatial Application 17 Spatial Application 18

3 R-Tree:Insert (cont.) R-Tree:Deletion

How to split full node
Different from deletion in B-tree in how to
Objective: reduce the number of node to be handle under-full (

Spatial Application 19 Spatial Application 20

R-Tree:Deletion (cont.) R-Tree:Update

How to shrink rectangle
Update is simple
Shrink to tightly contain all the entry
Delete original index from R-tree rectangles in the child node
Update the index
How to handle under-full node
Reinsert the index into the R-tree
Not merged with sibling
Other search operations are simply
Removed aside till the end and then entries variants of the one described arereinsertedintotheR-tree  Functionally equivalent with improve disk cache hit  Incrementally refine the spatial structure and prevent gradual deterioration due to permanently fixed parent-children relationship

Spatial Application 21 Spatial Application 22

R-Tree:Wrap-up Conclusion

Exploit strength of B-tree and geometry of
Spatial application is important, esp. in science and underlying objects engineering research
Dynamically update index
Conventional database technique failed to capture
Use heuristic optimization(linear algorithm) to bound overhead the essential nature of spatial application
Many variants have been proposed to
New methods and algorithms have been proposed, improve R-tree each trying to solve part of the problem
Hard to model continuous geo-spatial data such as a field (personal opinion)
No cure-all solution is perceived, which results in very active research in this area

Spatial Application 23 Spatial Application 24

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