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An x-fast trie containing the integers 1 (001 2), 4 (100 2) and 5 (101 2). Blue edges indicate descendant pointers. An x-fast trie is a bitwise trie: a binary tree where each subtree stores values whose binary representations start with a common prefix. Each internal node is labeled with the common prefix of the values in its subtree and ...
The AMT uses eight 32-bit bitmaps per node to represent a 256-ary trie that is able to represent an 8 bit sequence per node. With 64-Bit-CPUs (64-bit computing) a variation is to have a 64-ary trie with only one 64-bit bitmap per node that is able to represent a 6 bit sequence. Trie node with bitmap that marks valid child branches.
A notable variant is the bitwise trie, ... The following pseudocode implements the search procedure for a given string key in a rooted trie x. ... Statistics; Cookie ...
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process . [ 1 ]
An x-fast trie containing the integers 1 (001 2), 4 (100 2) and 5 (101 2), which can be used to efficiently solve the predecessor problem. One simple solution to this problem is to use a balanced binary search tree , which achieves (in Big O notation ) a running time of O ( log n ) {\displaystyle O(\log n)} for predecessor queries.
An alternative analysis arriving at the same approximation without the assumption of independence is given by Mitzenmacher and Upfal. [7] After all n items have been added to the Bloom filter, let q be the fraction of the m bits that are set to 0. (That is, the number of bits still set to 0 is qm.)
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
In computer science tree data structures, an X-tree (for eXtended node tree [1]) is an index tree structure based on the R-tree used for storing data in many dimensions. It appeared in 1996, [2] and differs from R-trees (1984), R+-trees (1987) and R*-trees (1990) because it emphasizes prevention of overlap in the bounding boxes, which increasingly becomes a problem in high dimensions.