Design, Implementation and Preliminary Analysis of General Multidimensional Trees

Abstract

In this thesis, a new multidimensional data structure, the q-kd tree, for storing points lying in a multidimensional space is defined, implemented and experimentally analyzed. This new data structure has k-d trees and quad-trees as particular cases. The main difference between q-kd trees and either kd-trees or quad-trees is the way in which discriminants are assigned to each node of the tree. While this is fixed for kd-trees and quad-trees, it is variable for q-kd trees. We propose two different ways for assigning discriminants to nodes, the heuristics: Split Tendency and Prob-of-1. These heuristics allow us to build what we call quasi-optimal q-kd trees and randomly-split q-kd trees respectively. Experimentally we show that our variants of q-kd trees are in between quad-trees and k-d trees concerning the memory space and internal path length, and that by proper parameter settings it is possible to construct q-kd trees taylored to the space and time restrictions we can have.