Slideshow:
4 common queries on multi-dimensional data:
(1) partial match query
4 common queries on multi-dimensional data:
(2) range query
4 common queries on multi-dimensional data:
(3) nearest neighbor query
4 common queries on multi-dimensional data:
(4) where-am-I query
Multi-dimensional indexes
Multi-dimensional indexes
- What are
some queries
that you can be
formulated on
multi-dimensional data ???
- Example 1:
Nearest point query
- Suppose we have a
relation containing
points
on a map
- Each point is stored
in the following relation:
Point( x, y )
- Given a
point p0(10, 20)
Query:
- Find the point that is closest to point p0(10, 20)
In SQL:
select * from Point P /* P is the closest point to p0 */ where not exists (select * from Point Q /* A closer point Q cannot exist ! */ where "distance(Q, p0) < distance(P, p0)")
select * from Point P /* P is the closest point to p0 */ where not exists (select * from Point Q /* A closer point Q cannot exist ! */ where (Q.x-10)2 + (Q.y-20)2 < (P.x-10)2 + (P.y-20)2 )
- Suppose we have a
relation containing
points
on a map
- Example 2:
containment query
- Suppose we have a
relation that define
rectanglar objects:
Rectangle( id, xll, yll, xur, yur )A rectangle can be represented (= defined) by the coordinates of the Lower Left and Upper Right points.
Example of representation of a rectangle:
- Given a point
P(10,20)
Query:
- Find all rectangles that contains the point P(10,20)
Answer in SQL:
select id from rectangle where xll ≤ 10 AND yll ≤ 20 AND 10 ≤ xur AND 20 ≤ yur
Graphically:
- Suppose we have a
relation that define
rectanglar objects:
-
Partial Match queries
- The query specifies conditions on some dimensions but not on all dimensions
Example:
- Find all points/objects that
intersects with
y = 50
-
Range queries
- Find objects that are located either partial or wholly within a certain range
Example:
- Find all objects that
have an overlap
with the
green area (= a range specification):
The green area can be specified as:
x1 ≤ x ≤ x2 y1 ≤ y ≤ y2
-
Nearest neighbor queries:
- Find object(s) that
is located
closest (nearest) to
a given point:
- Find object(s) that
is located
closest (nearest) to
a given point:
-
Where-am-I queries:
- Given a
location
(i.e., coordinate)
Find the object(s) that contains the location:
- Given a
location
(i.e., coordinate)
- Multi-dimensional index:
- Multi-dimensional index = an index on the multi-dimensional data that help us answer a (commonly used) multi-dimensional query (more) efficiently (= speedier)
- Before we
develop
such multi-dimensional
index, we
answer this
question first:
- Do we need
to develop
new
indexing techniques
for multi-dimensional data ????
I.e.: can't we use a one-dimensional index to help us answer (commonly used) multi-dimensional queries (more) efficiently (= speedier) ???
(If so, we don't need to do anything !!!!)
- Do we need
to develop
new
indexing techniques
for multi-dimensional data ????