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Tree::M - implement M-trees for efficient "metric/multimedia-searches"


  use Tree::M;

  $M = new Tree::M 


(not yet)

Ever had the problem of managing multi-dimensional (spatial) data but your database only had one-dimensional indices (b-tree etc.)? Queries like

 select data from table where latitude > 40 and latitude < 50
                          and longitude> 50 and longitude< 60;

are quite inefficient, unless longitude and latitude are part of the same spatial index (e.g. an R-tree).

An M-tree is an index tree that does not directly look at the stored keys but rather requires a distance (a metric, e.g. a vector norm) function to be defined that sorts keys according to their distance. In the example above the distance function could be the maximum norm (max(x1-x2, y1-y2)). The lookup above would then be something like this:

   my $res = $M->range([45,55], 5);

This module implements an M-tree. Although the data structure and the distance function is arbitrary, the current version only implements n-dimensional discrete vectors and hardwires the distance function to the suared euclidean metric (i.e. (x1-x2)**2 + (y1-y2)**2 + (z1-z2)**2 + ...). Evolution towards more freedom is expected ;)


$M = new Tree::M arg => value, ...

Creates a new M-Tree. Before it can be used you have to call one of the create or open methods below.

   ndims => integer
      the number of dimensions each vector has

   range => [min, max, steps]
      min      the lowest allowable scalar value in each dimension
      max      the maximum allowable number
      steps    the number of discrete steps (used when stored externally)

   pagesize => integer
      the size of one page on underlying storage. usually 4096, but
      large objects (ndims > 20 or so) might want to increase this

Example: create an M-Tree that stores 8-bit rgb-values:

   $M = new Tree::M ndims => 3, range => [0, 255, 256];

Example: create an M-Tree that stores coordinates from -1..1 with 100 different steps:

   $M = new Tree::M ndims => 2, range => [-1, 1, 100];

Open or create the external storage file $path and associate it with the tree.

[this braindamaged API will go away ;)]

$M->insert(\@v, $data)

Insert a vector (given by an array reference) into the index and associate it with the value $data (a 32-bit integer).


Synchronize the data file with memory. Useful after calling insert to ensure the data actually reaches stable storage.

$res = $M->range(\@v, $radius)

Search all entries not farther away from @v then $radius and return an arrayref containing the searchresults.

Each result is again anarrayref composed like this:

   [\@v, $data]

e.g. the same as given to the insert method.

$res = $M->top(\@v, $n)

Return the $n "nearest neighbours". The results arrayref (see range) contains the $n index values nearest to @v, sorted for distance.

$distance = $M->distance(\@v1, \@v2)

Calculcate the distance between two vectors, just as they databse engine would do it.

$depth = $M->maxlevel

Return the maximum height of the tree (usually a small integer specifying the length of the path from the root to the farthest leaf)


Inserting too many duplicate keys into the tree cause the C++ library to die, so don't do that.


Marc Lehmann <>.


perl(1), DBIx::SpatialKeys.