Properties
The min/max kdtree has - besides the properties of an kd-tree - the special property that an inner node's min/max values coincide each with a min/max value of either one child. This allows to discard the storage of min/max values at the leaf nodes by storing two bits at inner nodes, assigning min/max values to the children: Each inner node's min/max values will be known in advance, where the root node's min/max values are stored separately. Each inner node has besides two min/max values also two bits given, defining to which child those min/max values are assigned (0: to the left child 1: to the right child). The non-assigned min/max values of the children are the from the current node already known min/max values. The two bits may also be stored in the least significant bits of the min/max values which have therefore to be approximated by fractioning them down/up.
The resulting memory reduction is not minor, as the leaf nodes of full binary kd-trees are one half of the tree's nodes.
Read more about this topic: Min/max Kd-tree
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)