Prepare for your exams
Get points
Guidelines and tips
Sell on Docsity
Docsity AI

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Docsity AI

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Ranking in Spatial Database for Data Structures | CMSC 420, Study notes of Data Structures and Algorithms

University of Maryland Data Structures and Algorithms

Prof. Hanan Samet

Material Type: Notes; Professor: Samet; Class: Data Structures; Subject: Computer Science; University: University of Maryland; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

koofers-user-mvw 🇺🇸

10 documents

1 / 47

This page cannot be seen from the preview

Don't miss anything!

nn0

These notes may not be reproduced by any means (mechanical or elec-

tronic or any other) without the express written permission of Hanan Samet

RANKING IN SPATIAL DATABASES

GÍSLI R. HJALTASON

HANAN SAMET

COMPUTER SCIENCE DEPARTMENT AND

CENTER FOR AUTOMATION RESEARCH AND

INSTITUTE FOR ADVANCED COMPUTER STUDIES

UNIVERSITY OF MARYLAND

COLLEGE PARK, MARYLAND 20742-3411 USA

Discover Study notes of Data Structures and Algorithms University of Maryland

Partial preview of the text

Download Ranking in Spatial Database for Data Structures | CMSC 420 and more Study notes Data Structures and Algorithms in PDF only on Docsity!

nn

These notes may not be reproduced by any means (mechanical or elec- tronic or any other) without the express written permission of Hanan Samet

RANKING IN SPATIAL DATABASES

GÍSLI R. HJALTASON

HANAN SAMET

COMPUTER SCIENCE DEPARTMENT AND

CENTER FOR AUTOMATION RESEARCH AND

INSTITUTE FOR ADVANCED COMPUTER STUDIES

UNIVERSITY OF MARYLAND

COLLEGE PARK, MARYLAND 20742-3411 USA

nn

RANKING PROBLEM

Ex: Find all the houses in the database in the order of

their distance from locationp or objecto

Ex: Find the nearest city of population greater than 30,000 to Portland, Maine
If we use an index on the locational attributes corresponding to the location of the cities, then we want to obtain the cities in the order of their distance from Portland, Maine
The process ceases once the condition on the non- locational population attribute is satisfied
Query is also a partial ranking query
We are interested in a solution where if the closest record does not satisfy our query, then we can get the next clos- est record by continuing from where we last left off rather that having to restart from the reference point of the index
Used in browsing applications
1. can restrict query region
2. can vary nature of features retrieved as well as query object
3. can serve as basis of incremental spatial join operations
Our solution is illustrated by an example spatial index making use of a disjoint decomposition (e.g., PR quad- tree) although implemented for other spatial indexes including R-trees

nn

SPATIAL DATABASES

Distinguished from conventional databases, in part, by fact that some of the attributes are locational in which case they have a common dimensional unit which is distance in space
1. distance unit is the same whether we are in one, two, or three dimensions, etc.
2. if combine attributes and seek to find nearest record of

typet to Chicago, then unit is distance regardless of

whether there are one, two, three, ... (or even more)

locational attributes associated witht

nearest is not meaningful for combinations of non- locational attributes
not all attributes with type distance are locational (e.g., size corresponding to pant length, height, waist, etc.)

Spatial databases are differentiated by the type of records that they store

points (e.g., locations of features)

zero volumetric measure
discrete

features (i.e., space occupied by the features)

nonzero volumetric measure (i.e., extent)
continuous
Records in a conventional database are always discrete

can be viewed as points in a higher dimensional space
difference is that for spatial attributes, dimensional unit is always distance in space

nn

ORDERING DATA

Use a combination of the values of the locational attributes
Facilitates storage of records
Desirable for ordering to preserve proximity — i.e., records close to each other in the multidimensional space should also be close to each other in the ordering
Hashing is a way of achieving ordering
1. explicit order
  - mapping from higher dimensional space to one- dimensional space
  - e.g., bit interleaving (Morton order), Peano-Hilbert, Sierpinski, etc.
  - result is a space-filling curve
  - no order has property that ALL records that are close to each other in the multidimensional space of the locational attributes are also close to each other in the range of the mapping
2. implicit order
  - bucketing methods
  - sort records on the basis of the space they occupy and group into cells or buckets of finite capacity

nn R-TREES

Objects grouped into hierarchies, stored in another structure such as a B-tree

Object has single bounding rectangle, yet area that it spans may be included in several bounding rectangles

Does not result in disjoint decomposition of space

a

b

c

d

e

f

g

h

i

1 b

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node

except root

(^) at least 2 entries in root unless a leaf node

nn R-TREES

Objects grouped into hierarchies, stored in another structure such as a B-tree

Object has single bounding rectangle, yet area that it spans may be included in several bounding rectangles

Does not result in disjoint decomposition of space

a

b

c

d

e

f

g

h

i

1 b

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node

except root

(^) at least 2 entries in root unless a leaf node

(^2) nn r

R

R R

nn R-TREES

Objects grouped into hierarchies, stored in another structure such as a B-tree

Object has single bounding rectangle, yet area that it spans may be included in several bounding rectangles

Does not result in disjoint decomposition of space

a

b

c

d

e

f

g

h

i

1 b

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node

except root

(^) at least 2 entries in root unless a leaf node

(^2) nn r

R

R R

(^3) nn z

R3 R4 R5 R

R

R1: R2:

(^4) nn g

R0: R1 R

R

nn SEARCHING FOR A POINT OR LINE SEGMENT IN AN R-TREE

1 b

a b d g h c i e f

R1 R

R3 R4 R5 R

a

b

c

d

e

f

g

h

i

R

R R

R2 R

R

Q

May have to examine many nodes since a line segment can be contained in the covering rectangles of many nodes yet its record is contained in only one leaf node (e.g., i in R2, R3, R4, and R5)

Ex: Search for a line segment containing point Q

R3: R4: R5: R6:

R1: R2:

R0:

R

nn SEARCHING FOR A POINT OR LINE SEGMENT IN AN R-TREE

1 b

a b d g h c i e f

R1 R

R3 R4 R5 R

a

b

c

d

e

f

g

h

i

R

R R

R2 R

R

Q

May have to examine many nodes since a line segment can be contained in the covering rectangles of many nodes yet its record is contained in only one leaf node (e.g., i in R2, R3, R4, and R5)

Ex: Search for a line segment containing point Q

R3: R4: R5: R6:

R1: R2:

R0:

R

nn

Q is in R

2 v

nn

Q can be in both R1 and R

3 r

nn SEARCHING FOR A POINT OR LINE SEGMENT IN AN R-TREE

1 b

a b d g h c i e f

R1 R

R3 R4 R5 R

a

b

c

d

e

f

g

h

i

R

R R

R2 R

R

Q

May have to examine many nodes since a line segment can be contained in the covering rectangles of many nodes yet its record is contained in only one leaf node (e.g., i in R2, R3, R4, and R5)

Ex: Search for a line segment containing point Q

R3: R4: R5: R6:

R1: R2:

R0:

R

nn

Q is in R

2 v

nn

Q can be in both R1 and R

3 r

(^4) nn z

Searching R1 first means that R4 is searched but this leads to failure even though Q is part of i which is in R

nn DISJOINT CELLS

Objects decomposed into disjoint subobjects; each subobject in different cell

Drawback: in order to determine area covered by object, must retrieve all cells that it occupies

Techniques differ in degree of regularity

R+-tree (also k-d-B-tree) and cell tree are examples of this technique

a

b

c

d

e

f

g

h

i

1 b

Q

nn DISJOINT CELLS

Objects decomposed into disjoint subobjects; each subobject in different cell

Drawback: in order to determine area covered by object, must retrieve all cells that it occupies

Techniques differ in degree of regularity

R+-tree (also k-d-B-tree) and cell tree are examples of this technique

a

b

c

d

e

f

g

h

i

1 b

Q

(^2) nn r

R R

R

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

nn DISJOINT CELLS

Objects decomposed into disjoint subobjects; each subobject in different cell

Drawback: in order to determine area covered by object, must retrieve all cells that it occupies

Techniques differ in degree of regularity

R+-tree (also k-d-B-tree) and cell tree are examples of this technique

a

b

c

d

e

f

g

h

i

1 b

Q

(^2) nn r

R R

R

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

(^3) nn z

R3 R4 R5 R

R

R1: R2:

(^4) nn g

R0: R1 R

R

nn

UNIFORM GRID

Ideal for uniformly distributed data
Supports set-theoretic operations
Spatial data (e.g., line segment data) is rarely uniformly distributed

Ranking in Spatial Database for Data Structures | CMSC 420, Study notes of Data Structures and Algorithms

Related documents

Partial preview of the text

Download Ranking in Spatial Database for Data Structures | CMSC 420 and more Study notes Data Structures and Algorithms in PDF only on Docsity!

RANKING IN SPATIAL DATABASES

GÍSLI R. HJALTASON

HANAN SAMET

COMPUTER SCIENCE DEPARTMENT AND

CENTER FOR AUTOMATION RESEARCH AND

INSTITUTE FOR ADVANCED COMPUTER STUDIES

UNIVERSITY OF MARYLAND

COLLEGE PARK, MARYLAND 20742-3411 USA

their distance from locationp or objecto

typet to Chicago, then unit is distance regardless of

locational attributes associated witht

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node

Order (m,M ) R-tree

1. betweenm M/2 andM entries in each node