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A data tree is one of the data structures that are used in organizing data. With the binary tree being the basic form, data tree has an inherent hierarchy and looks like an inverted tree. From the root, the nodes or vertices branch out until a leaf is reached (Sherrod, 2007). This data structure is similar to the tree directory structure, which is the most popular as it is used in Windows and Linux operating system (‘Tree structured directories,’ 2013). The data trees that are compared in this discussion are the segment tree and suffix tree.

A segment tree is a binary tree that is implemented when a number of queries such as minimum, maximum, sum, and producthave to be made to a set of numerical values contained in an array. The array elements are represented by the leaves and these values are traversed in postorder. This process adds the values of two children nodes such that the parent nodes represent the sum. Each parent node is labeled with the interval of the indices of array elements that are added to get the sum at the parent node (Smit, n.d.).

A suffix tree is a compressed trie of all suffixes in a text and is used primarily in finding all instances of a pattern. It can also search for the longest repeated substring, the longest common substring, and the longest palindrome in a string. The search requires the preprocessing of the text in order to allow a search through time linear as a function of pattern length. Examples of pattern searching algorithms that use an amount of time proportional to the text length are KMP and Z. The advantage of using a suffix tree in Ctrl + F function is due to the pattern length that is typically shorter than the text length. A suffix tree is a non-binary tree with nodes that represent all the suffixes in the given text. The compressed trie is built with the suffixes that are considered as individual words

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A data tree is one of the data structures that are used in organizing data. With the binary tree being the basic form, data tree has an inherent hierarchy and looks like an inverted tree. From the root, the nodes or vertices branch out until a leaf is reached (Sherrod, 2007). This data structure is similar to the tree directory structure, which is the most popular as it is used in Windows and Linux operating system (‘Tree structured directories,’ 2013). The data trees that are compared in this discussion are the segment tree and suffix tree.

A segment tree is a binary tree that is implemented when a number of queries such as minimum, maximum, sum, and producthave to be made to a set of numerical values contained in an array. The array elements are represented by the leaves and these values are traversed in postorder. This process adds the values of two children nodes such that the parent nodes represent the sum. Each parent node is labeled with the interval of the indices of array elements that are added to get the sum at the parent node (Smit, n.d.).

A suffix tree is a compressed trie of all suffixes in a text and is used primarily in finding all instances of a pattern. It can also search for the longest repeated substring, the longest common substring, and the longest palindrome in a string. The search requires the preprocessing of the text in order to allow a search through time linear as a function of pattern length. Examples of pattern searching algorithms that use an amount of time proportional to the text length are KMP and Z. The advantage of using a suffix tree in Ctrl + F function is due to the pattern length that is typically shorter than the text length. A suffix tree is a non-binary tree with nodes that represent all the suffixes in the given text. The compressed trie is built with the suffixes that are considered as individual words.

A search tree is a special type of tree that is used to guide the search for a record, given
the value of one of the record's fields.The index
field values in each node guide us to the next node, until we reach the data file block that
contains the required records. By following a pointer, we restrict our search at each level
to a subtree of the search tree and ignore all nodes not in this subtree.

B-Trees. The B-tree has additional constraints that ensure that the tree is always
balanced and that the space wasted by deletion, if any, never becomes excessive. The algorithms for insertion and deletion, though, become more complex in order to maintain
these constraints. Nonetheless, most insertions and deletions are simple processes; they
become complicated only under special circumstances-namely, whenever we attempt an
insertion into a node that is already full or a deletion from a node that makes it less than
half full. More formally, a Btree of order p, when used as an access structure on a key field
to search for records in a data file.Once the root node is full with p - 1 search key values and we attempt to insert another
entry in the tree, the root node splits into two nodes at level 1. Only the middle value is
kept in the root node, and the rest of the values are split evenly between the other two
nodes. When a nonroot node is full and a new entry is inserted into it, that node is split
into two nodes at the same level, and the middle entry is moved to the parent node along
with two pointers to the new split nodes. If the parent node is full, it is also split. Splitting
can propagate all the way to the root node, creating a new level if the root is split.

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