Thuyết trình cơ sở dữ liệu nâng cao point access method

• Each cell is associated with one bucket, but a bucket may contain several adjacent cells • Since the directory may grow large, it is usually kept on secondary storage • To guarantee t

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Point Access Method

1 Spatial Data

2 Main Memory Structure

3 Point Access Methods

Point Access Method

Spatial Data

• Complex Structure

• Dynamic

• Spatial databases tend to be large

• There is no standard algebra defined on spatial data

• Many spatial operators are not closed

• Spatial database operators more expensive than standard relational operators

• There is no total order among spatial object

Characteristic of Spatial Data

Queries in Spatial Data

• Exact Match Query ( EMQ )

• Condition : Given object o’ with spatial extent o’.G in Euclide with d-dimension

• Target : Find all objects o with same spatial extent as o’

• Query

• Point Query (PQ )

• Condition : Given a point p in Euclide with d-dimension

• Target : Find all objects o ovelapping with p

• Query

Queries in Spatial Data

• Enclosure Query ( EQ )

• Condition : Given object o’ with spatial extent o’.G in Euclide with d-dimension

• Target : Find all objects o enclosing o’

• Query

Queries in Spatial Data

• Requirements for Multidimensional Access Methods

• Dynamics

• Secondary/tertiary storage management

• Broad range of supported operations

• Independence of the input data and insertion sequence

Main Memory Structure

ith point: pi ith polygon: ri ith centroid: ci ith minimum bounding

box: mi

Figure 9 Running example.

Main Memory Structure

ith point: pi ith polygon: ri ith centroid: ci ith minimum bounding

box: mi

Figure 9 Running example.

Main Memory Structure

ith point: pi ith polygon: ri ith centroid: ci ith minimum bounding

box: mi

Figure 10 k-d construction

Main Memory Structure

ith point: pi ith polygon: ri ith centroid: ci ith minimum bounding

box: mi

Figure 11 k-d tree

Main Memory Structure

• Designed for main memory applications where all the data are available without accessing the disk

• Do not take secondary storage management into account explicitly

• In many spatial database applications the amount of data to be managed is notoriously large

• Multidimensional Hashing

• Hierarchical Access Method

Point Access Methods

• No total order for objects in two- and higher-dimensional space that completely preserves spatial proximity

• Try to construct hashing functions that preserve proximity at least to some extent

• Goal: Objects located close to each other in original space should be likely to be stored close together on the disk

• =>minimizing the number of disk accesses per range query

Multidimensional Hashing

• A d-dimensional orthogonal grid on the universe.

• The grid is not necessarily regular, the resulting cells may be of different shapes and sizes.

• Each cell is associated with one bucket, but a bucket may contain several adjacent cells

• Since the directory may grow large, it is usually kept on secondary storage

• To guarantee that data items are always found with no more than two disk accesses for exact match queries, the grid itself is kept in main memory, represented by d one-dimensional arrays called scales

The Grid File

• decomposes the universe regularly: all grid cells are of equal size

• each new split results in the halving of all cells and therefore in the doubling of the directory size

EXCELL

• Use a second grid file to

manage the grid directory

• The first of the two levels is called the root directory,

• Second level: the actual grid directory

• root directory contain

• pointers to the directory

pages of the lower level,

which in turn contain

pointers to the data pages

• Splits are often confined to the subdirectory regions

without affecting too much the surroundings

• =>slower directory growth

• not solve the problem of

super linear directory size

The Two-Level Grid File

• increase space utilization by introducing a second grid file

• relationship between these two grid files is not hierarchical but somewhat more balanced

• Both grid files span the whole universe

• The distribution of the data among the two files is performed dynamically

The Twin Grid File

• Based on binary of multi-way tree structure

• like hashing, stores data in bucket

• each bucket is leaf of a node, and a disk page

• interior nodes of the tree guide search

• search: top-down tree traversal

• difference between different methods: characteristics of the regions

Hierarchical Access Method

• k-d-B-tree

• combination of adaptive k-d-tree and B-tree

• partition the universe like adaptive k-d

• associates subspaces to tree nodes

• interior nodes are intervals

• nodes in same level are mutually disjoint

• perfectly balanced (like B-tree)

• search straightforward, like k-d-tree

• insert: search, find the right bucket, if required split and move half the data to it.

• Deletion: search, remove, if necessary merge node with siblings

Hierarchical Access Method

• k-d-B-tree

• combination of adaptive k-d-tree and B-tree

• partition the universe like adaptive k-d

• associates subspaces to tree nodes

• interior nodes are intervals

• nodes in same level are mutually disjoint

• perfectly balanced (like B-tree)

• search straightforward, like k-d-tree

• insert: search, find the right bucket, if required split and move half the data to it.

• Deletion: search, remove, if necessary merge node with siblings

Hierarchical Access Method

• LSD tree

• directory is organized same as adaptive k-d-tree

• better adaptation to data distribution (in compare to fixed binary partitioning)

• external balancing property: heights of external subtrees differ at most by one

• combines two split strategies to accommodate skewed data:

• data-dependent : based on data, tries to achieve most balanced structure (equal number of data in both sides of split)

• distribution-dependent: split at fixed dimension and position (know distribution is assumed)

Hierarchical Access Method

•Buddy tree:

• dynamic hashing scheme with tree structure (hybrid)

• tree is made by consecutive insertions

• cut the universe equally with iso-oriented hyperplanes

• interior nodes: a partition and an interval (MBB of points or intervals below node)

• intervals in same level nodes are mutually disjoint

• leaves are data (like other trees!!)

• each directory node has at least two entries

=> may not be balanced

• when a node splits, MBB of two intervals are computed to reflect the current situation

=> tries to achieve high selectivity at directory level

• except for root, only one pointer refers to each directory page

=> guarantees linear growth

Hierarchical Access Method

• BANG file (Balanced and Nested Grid)

• a hybrid method

• divides the univers to intervals (boxes), similar to grid

• difference: buckets regions may intersect

• can form nonrectangular bucket regions by taking geometric difference of two intervals (nesting)

• increased storage utilization: redistributes data between bucket during insertion

• balanced search tree to manage directory

Hierarchical Access Method

• BANG file (Balanced and Nested Grid)

• first 3 rectangles: R1: R2, R5, R6

• then R3 and R4 in R2 and R5

• representation as bit interleaving

• * = universe

• a point search may require traversal of entire directory in depth-first manner

Hierarchical Access Method

• hB-tree

• utilizes k-d-B-tree to organize the space represented by interior nodes

• difference in splitting: based on multiple attributes

• region not boxed shape

Hierarchical Access Method

• BV-tree

• tries to solve d-dimensional B-tree

• idea: maintain major strengths of Btree, by relaxing balancing and space utilization

• BV-tree not balanced

• at least 33% space utilization (50% for B-tree)

• What form of Point Query in Spatial Data ?

• What methods belong to Multidimensional Hashing Method?

• Grid File

• K-d Tree

• Linear Hashing

• EXCELL