Tree-Independent Dual-Tree Algorithms

Ryan Curtin, William March, Parikshit Ram, David Anderson, Alexander Gray, Charles Isbell
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1435-1443, 2013.

Abstract

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-curtin13, title = {Tree-Independent Dual-Tree Algorithms}, author = {Curtin, Ryan and March, William and Ram, Parikshit and Anderson, David and Gray, Alexander and Isbell, Charles}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1435--1443}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/curtin13.pdf}, url = {https://proceedings.mlr.press/v28/curtin13.html}, abstract = {Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.} }
Endnote
%0 Conference Paper %T Tree-Independent Dual-Tree Algorithms %A Ryan Curtin %A William March %A Parikshit Ram %A David Anderson %A Alexander Gray %A Charles Isbell %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-curtin13 %I PMLR %P 1435--1443 %U https://proceedings.mlr.press/v28/curtin13.html %V 28 %N 3 %X Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.
RIS
TY - CPAPER TI - Tree-Independent Dual-Tree Algorithms AU - Ryan Curtin AU - William March AU - Parikshit Ram AU - David Anderson AU - Alexander Gray AU - Charles Isbell BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-curtin13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 1435 EP - 1443 L1 - http://proceedings.mlr.press/v28/curtin13.pdf UR - https://proceedings.mlr.press/v28/curtin13.html AB - Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings. ER -
APA
Curtin, R., March, W., Ram, P., Anderson, D., Gray, A. & Isbell, C.. (2013). Tree-Independent Dual-Tree Algorithms. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):1435-1443 Available from https://proceedings.mlr.press/v28/curtin13.html.

Related Material