高維下的 kd-tree

　
http://www.codeproject.com/KB/architecture/KDTree.aspx

Anton Milev 文中寫到：

For small dimensions the KD-tree can be much faster then sequential search, however for 10-dimensional space the checked nodes for rises to about 25% for. It is possible to reduce this number 2-3 times if the tree is balanced but the tendency of exponential rise of the checked nodes makes the KD unpracticle above 15 dimensions. The second curve shows how KD / Brute ratio changes with space dimension, Brute stands for sequential search, it checks all nodes. Practiclly, for 10000 points, the KD tree becomes as fast as the sequential search for dimensions bigger then 10.

With the analyses made in this article I showed that the standard KD-tree is not good for dimensions beyond 10. In my next article about KD trees and the nearest neighbours search in N-dimensions I will introduce an extention of the quad tree for N-dimensional data - QD-tree, it is faster then KD and allows run-time balancing. However for big dimensions it again becomes slow. This problem is well known in the computational geometry, this would be so for any data structure based only on tree. From another hand it is not possible to make a multidimensional linked-list and to include it in the tree. The problem is quite complicated and requires new kinds data structures.