Multidimensional Index Multidimensional Index StructuresStructures

One dimensional index structures assume One dimensional index structures assume a single search key, and retrieve records a single search key, and retrieve records that match a given search-key value. (The that match a given search-key value. (The search key can be a single field or a search key can be a single field or a combination of fields.)combination of fields.)

Many applications, e.g. GIS, OLAP, Many applications, e.g. GIS, OLAP, require us to view data as existing in a require us to view data as existing in a space of two or more dimensions.space of two or more dimensions.

Multidimensional Index Multidimensional Index StructuresStructures

The queries to be supported on such data:The queries to be supported on such data: partial-match queriespartial-match queries: specify values for a : specify values for a

subset of the dimensionssubset of the dimensions range queriesrange queries: give the range for each : give the range for each

dimension.dimension. nearest-neighbor queriesnearest-neighbor queries: ask for the closest : ask for the closest

point to the given point.point to the given point.

Grid FileGrid File

The grid file slices the space of points in The grid file slices the space of points in each of the dimensions.each of the dimensions.

Each of the regions can be thought of as a Each of the regions can be thought of as a bucket, and each of the points in that bucket, and each of the points in that region has its record placed in a block region has its record placed in a block belonging to that bucket. If needed, belonging to that bucket. If needed, overflow blocks can be used to increase overflow blocks can be used to increase the size of a bucket.the size of a bucket.

Age Salary 26 60 45 60 50 75 50 100 50 120 70 110 85 140 30 260 25 400 45 350 50 275 60 260

*

**

** *

***

*

**

0 40 55 100

500

225

90

0

Age

Salary

25, 60

25, 400

30, 260

50, 75

45, 60

50, 120

50, 100

50, 275

85, 140

70, 110

45, 350

60, 260

0-40 40-55 55+ 225+

90-225

0-90

SearchingSearching

A grid directory consists of a A grid directory consists of a kk--dimensional array (dimensional array (grid arraygrid array) and k one-) and k one-dimensional arrays (dimensional arrays (linear scaleslinear scales).).

To search for a record:To search for a record: determine the positions of the record in each determine the positions of the record in each

of the dimensions according to the of the dimensions according to the linear linear scalesscales

locate the proper bucket in the locate the proper bucket in the grid arraygrid array access the data blockaccess the data block

InsertionInsertion

Locate the bucket for the new record, then Locate the bucket for the new record, then place the record in the block of the bucket place the record in the block of the bucket if there is room.if there is room.

If no room, two general approaches:If no room, two general approaches: add an overflow block as needed; add an overflow block as needed; refine the grid partition by splitting blocks; refine the grid partition by splitting blocks;

there is a choice of dimension and point of there is a choice of dimension and point of split.split.

PerformancePerformance

Assumption:Assumption: the bucket matrix can be kept in main memorythe bucket matrix can be kept in main memory the array of partitioning values in each the array of partitioning values in each

dimension can be kept in main memorydimension can be kept in main memory Point queryPoint query

the number of I/O’s is what is necessary to the number of I/O’s is what is necessary to read the bucket. read the bucket.

For insertion and deletion, an additional disk For insertion and deletion, an additional disk write is needed.write is needed.

More about Grid FileMore about Grid File

Partial-match queryPartial-match query Range queryRange query Nearest-neighbor queryNearest-neighbor query Reference:Reference:

J. Nievergelt, et al., “The grid file: an J. Nievergelt, et al., “The grid file: an adaptable, symmetric, multikey file structure”, adaptable, symmetric, multikey file structure”, ACM Trans. on Database Systems 9:1(1984), ACM Trans. on Database Systems 9:1(1984), pp. 38-71.pp. 38-71.