Slideshow:
Performance of Grid index for the commonly used
multi-dimensional queries
Partial match queries
Partial match queries
Partial match queries
Range queries
Nearest neighbor queries
How can we use the Grid Index to find the nearest neighbor (point) (search ?)
The "Expanding Search" Algorithm
(pruning)
We use the nearest neight candidate to prune the search space
The "Expanding Search" Algorithm
(pruning)
The "Expanding Search" Algorithm
(pruning)
The "Expanding Search" Algorithm
(pruning)
The "Expanding Search" Algorithm
(pruning)
The "Expanding Search" Algorithm
(pruning)
The "Expanding Search" Algorithm
(pruning)
"Where-am-I" queries
"Where-am-I" queries
- Assumption:
- The grid index file can be
stored
entirely
in memory
I.e.: there is no disk accesses needed to search the grid index file
- The grid index file can be
stored
entirely
in memory
-
Performance
of a Grid index in
Partial Match queries
- A Partial Match query specifies conditions on some dimensions but not on all dimensions
Example:
- Find all jewelry purchases by
people with
age = 50
Conclussion:
- You will access
m disk blocks
(m is some dimension of the grid)
Note:
- We access fewer disk blocks because "geographically related" data are stored in the same grid bucket !!!
-
Performance
of a Grid index in
Range queries
- Find all objects that are located either partial or wholly inside a certain area
Example:
- Find all jewelry purchases
by people whose:
35 ≤ age ≤ 50 50K ≤ salary ≤ 100KSolution:
In this example, we must access 4 disk blocks
-
Performance
of a Grid index in
Nearest neighbor queries:
Find the nearest neighbor of a data point:
Use the expanding range search algorithm:
- Start by
finding the nearest neighbor
in the
bucket that contains the
data point:
Nearest neighbor candidate:
- Nearest neighbor candidate =
the nearest neightbor found
so far
in the search
- Search distance = the distance of the nearest neighbor candidate to the search data point
- Nearest neighbor candidate =
the nearest neightbor found
so far
in the search
- Limit the
search space:
- Use
the search distance to
limit the
grid index buckets where you
need to search
to find the nearest neighbor:
- Draw a
disk around
the data point
( (age − agep)2 + (salary − salaryp)2 ≤ search-distance2 )
Example:
- Limit the
search space to
the grid index buckets that
intersects with the
disk:
- Draw a
disk around
the data point
- Use
the search distance to
limit the
grid index buckets where you
need to search
to find the nearest neighbor:
- Proceed to
search in the
first "candidate" grid index bucket
that is
intersects
the disk:
- When you find a
better nearest nighbor:
You re-compute the (smaller) search distance:
And limit the search space further:
- When you find a
better nearest nighbor:
- And so forth
- Start by
finding the nearest neighbor
in the
bucket that contains the
data point:
- Performance:
- The expanding range search will
access an
average of about
9 grid buckets
(in a 2-dimensional grid index):
- The expanding range search will
access an
average of about
9 grid buckets
(in a 2-dimensional grid index):
-
Performance
of a Grid index in
Where-am-I queries:
- Given a
location
(i.e., coordinate)
Find the object(s) that contains the location:
- The Grid index
cannot
represent objects
(can only
present points)
- The Grid Index cannot handle Where-am-I type of queries !!!
In fact, the only kind of index that can handle Where-am-I queries is:
- The R-tree (Region-tree)
(Discussed later)
- Given a
location
(i.e., coordinate)