Multidimensional Index Structures

1
Multidimensional Index Structures

• One dimensional index structures assume a single
  search key, and retrieve records that match a
  given search-key value. (The search key can be a
  single field or a combination of fields.)
• Many applications, e.g. GIS, OLAP, require us to
  view data as existing in a space of two or more
  dimensions.

2
Multidimensional Index Structures

• The queries to be supported on such data
• partial-match queries specify values for a
  subset of the dimensions
• range queries give the range for each dimension.
• nearest-neighbor queries ask for the closest
  point to the given point.

3
Grid File

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

4
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
5
0-40 40-55 55
225 90-225 0-90
60, 260
25, 60
50, 100
70, 110
50, 120
85, 140
30, 260
45, 350
45, 60
50, 275
25, 400
50, 75
6
Searching

• A grid directory consists of a k-dimensional
  array (grid array) and k one-dimensional arrays
  (linear scales).
• To search for a record
• determine the positions of the record in each of
  the dimensions according to the linear scales
• locate the proper bucket in the grid array
• access the data block

7
Insertion

• Locate the bucket for the new record, then place
  the record in the block of the bucket if there is
  room.
• If no room, two general approaches
• add an overflow block as needed
• refine the grid partition by splitting blocks
  there is a choice of dimension and point of split.

8
Performance

• Assumption
• the bucket matrix can be kept in main memory
• the array of partitioning values in each
  dimension can be kept in main memory
• Point query
• the number of I/Os is what is necessary to read
  the bucket.
• For insertion and deletion, an additional disk
  write is needed.

9
More about Grid File

• Partial-match query
• Range query
• Nearest-neighbor query
• Reference
• J. Nievergelt, et al., The grid file an
  adaptable, symmetric, multikey file structure,
  ACM Trans. on Database Systems 91(1984), pp.
  38-71.