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Multi-Dimensional Data Structure (mdds)

A collection of multi-dimensional data structure and indexing algorithm.

Overview of data structures included in mdds

This library implements the following data structure:

  • segment_tree
  • flat_segment_tree
  • rectangle_set
  • point_quad_tree
  • multi_type_vector
  • multi_type_matrix
  • sorted_string_map
  • trie_map
  • packed_trie_map

Segment Tree

Segment tree is a balanced-binary-tree based data structure efficient for detecting all intervals (or segments) that contain a given point.
The segments may overlap with each other. The end points of stored segments are not inclusive, that is, when an interval spans from 2 to 6, an arbitrary point x within that interval can take a value of 2 <= x < 6.

Flat Segment Tree

Flat segment tree is a variant of segment tree that is designed to store a collection of non-overlapping segments. This structure is efficient when you need to store values associated with 1 dimensional segments that never overlap with each other. Like segment tree, stored segments' end points are non-inclusive.

Rectangle Set

Rectangle set stores 2-dimensional rectangles and provides an efficient way to query all rectangles that contain a given point in 2-dimensional space. It internally uses nested segment tree. Each rectangle is defined by two 2-dimensional points: the top-left and bottom-right points, and the bottom-right point is non-inclusive. For instance, if a rectangle ranges from (x=2, y=2) to (x=10, y=20), then a 2-dimension point A (x,y) is said to be inside that rectangle only when 2 <= x < 10 and 2 <= y < 20.

Point Quad Tree

Point quad tree stores 2-dimensional points and provides an efficient way to query all points within specified rectangular region.

Multi Type Vector

Multi-type vector allows storage of unspecified number of types in a single logical array such that contiguous elements of identical type are stored in contiguous segment in memory space.

Multi Type Matrix

Multi-type matrix is a matrix structure that allows storage of four different element types: numeric, string, boolean and empty. It uses multi-type vector as its underlying storage.

Sorted String Map

Sorted string map is a simple data structure that takes a pre-sorted list of key-value pairs that are known at compile time, and allows efficient lookup. It does not allocate memory to duplicate its content, as it directly uses the pre-sorted list provided by the caller.

Trie Map

Trie map is an associative container that stores multiple key-value pairs where keys are stored in a trie structure to optimize for prefix searches.

Packed Trie Map

Packed trie map is nearly identical to the trie map counterpart except that this one is immutable. It packs all its content in a contiguous array for optimum storage and lookup efficiency.

API Documentation


mdds is free software. You may copy, distribute, and modify it under the terms of the License contained in the file COPYING distributed with this package. This license is the same as the MIT/X Consortium license.


Version API Version Release Date Download Check Sum File Size (bytes)
1.2.2 1.2 2016-09-09 mdds-1.2.2.tar.bz2 sha256sum: 141e730b39110434b02cd844c5ad3442103f7c35f7e9a4d6a9f8af813594cc9d 286185
1.2.1 1.2 2016-06-23 mdds-1.2.1.tar.bz2 sha256sum: 1e2f49dfc7b9d444bad07064837099741f4c2d061807173392ad2357116dfc7b 285426
1.2.0 1.2 2016-05-11 mdds-1.2.0.tar.bz2 sha256sum: f44fd0635de94c7d490f9a65f74b5e55860d7bdd507951428294f9690fda45b6 284962
1.1.0 1.0 2016-02-10 mdds-1.1.0.tar.bz2 sha256sum: 4253ab93fe8bb579321a50e247f1f800191ab99fe2d8c6c181741b8bd3fb161f 258691
1.0.0 1.0 2015-10-06 mdds_1.0.0.tar.bz2 sha256sum: ef8abc1236b54c7ca16ae1ee38abfb9cdbc5d1e6a2427c65b92b8c1003e3bf56 166619
0.12.1 2015-06-11 mdds_0.12.1.tar.bz2 md5sum: ef2560ed5416652a7fe195305b14cebe
sha1sum: e7469349f8d0c65545896fe553918f3ea93bd84d
0.12.0 2015-02-05 mdds_0.12.0.tar.bz2 md5sum: 17edb780d4054e4205cd956910672b83
sha1sum: 043590edde76a1df3e96070c46cbc7ae5f88f081
0.11.2 2014-12-18 mdds_0.11.2.tar.bz2 md5sum: cb4207cb913c7a5a8bfa5b91234618ee
sha1sum: 17d2d06a1df818de61bba25a9322541e80f6eed7
0.11.1 2014-10-02 mdds_0.11.1.tar.bz2 md5sum: 896272c1a9e396b871cb4dffbd694503
sha1sum: 0c1ace97ad310e5293c538f395176d9a506cdeda
0.11.0 2014-09-18 mdds_0.11.0.tar.bz2 md5sum: a67a46ec9d00d283a7cd8dbdd2906b59
sha1sum: cefd57cf7cd0408737b3d76ed0771694f26bda58
0.10.3 2014-04-23 mdds_0.10.3.tar.bz2 md5sum: aa5ca9d1ed1082890835afab26400a39
sha1sum: 0c4fa77918b8cc8ad32460c8d8a679e065976dbe
0.10.2 2014-02-12 mdds_0.10.2.tar.bz2 md5sum: 47203e7cade74e5c385aa812f21e7932
sha1sum: 26027170f7cdf7a4dcc39ea01376d394dcd21ffc
0.10.1 2014-01-08 mdds_0.10.1.tar.bz2 md5sum: 01a380acfec23bf617117ce98e318f3d
sha1sum: 199e609afa5ae08d164754f7a0a54b01f88692d0
0.10.0 2014-01-03 mdds_0.10.0.tar.bz2 md5sum: 26272a8e8c984d21ba800b4edcd3ada8
sha1sum: 2234e98f9e36041d0a41f037f628f2178f707307
0.9.1 2013-10-21 mdds_0.9.1.tar.bz2 md5sum: 8c853024fbcff39113d9285250dafc66
sha1sum: d80f6b74827d5e36ecbb8975b0f8f42896162d95

Older releases are archived here.


Once you have downloaded the package, run the following commands to install the mdds headers to your system:

tar xvf mdds_<version>.tar.bz2
cd mdds_<version>
make check  # optional for executing tests.
make install

It will install the headers under /usr/local by default. Use the --prefix option of the script to specify custom install location if you wish to install it to a non-default location.

API Incompatibility Notes


trie_map / packed_trie_map

  • The find() method now returns a const_iterator instance rather than a value type. It returns an end position iterator when the method fails to find a match.

  • The prefix_search() method now returns a search_results instance that has begin() and end() methods to allow iterating through the result set.

  • The constructor no longer takes a null value parameter.

  • Some nested type names have been renamed:

    • string_type -> key_type
    • char_type -> key_unit_type
    • string_buffer_type -> key_buffer_type
  • Some functions expected from the key trait class have been renamed:

    • init_buffer() -> to_key_buffer()
    • to_string() -> to_key()
  • The kay trait class now expects the following additional static methods:

    • key_buffer_type to_key_buffer(const key_type& key)
    • key_unit_type* buffer_data(const key_buffer_type& buf)
    • size_t buffer_size(const key_buffer_type& buf)


  • The search_result nested class has been renamed to search_results, to keep the name consistent with that of the same name in trie_map and packed_trie_map.


  • The matrix trait structure (formerly known as the string trait structure) now needs to specify the type of block that stores integer values as its integer_element_block member.


  • Starting with version 1.0, mdds now requires support for C++11. Stick with 0.12 or earlier versions if you use a compiler that doesn't support C++11.

  • data_type has been renamed to value_type for segment_tree, rectangle_set, and point_quad_tree.



  • The number of template parameters in custom_block_func1, custom_block_func2 and custom_block_func3 have been reduced by half, by deducing the numerical block type ID from the block type definition directly. If you use the older variant, simply remove the template arguments that are numerical block IDs.



  • The search_tree() method in 0.8.0 returns std::pair instead of just returning bool as of 0.7.1. If you use this method and relies on the return value of the old version, use the second parameter of the new return value which is equivalent of the previous return value.



  • The search() method now returns ::std::pair. This method previously returned only bool. Use the second parameter of the new return value which is equivalent of the previous return value.

Who uses mdds?

These are the projects that are known to use mdds.