The Trie Data Structure

1
The Trie Data Structure

• Basic definition a recursive tree structure that
  uses the digital decomposition of strings to
  represent a set of strings for searching.
• Example
• One of the advantages of the trie data structure
  is that its tree depth depends on the amount of
  data stored in it. Each element of data is stored
  at the highest level of the tree that still
  allows a unique retrieval.

2
Another Trie Example

• Suppose we have a string that can be identified
  by the number sequence 8376. Assume also that the
  trie data structure consists of a trie array at
  the top level. If 8376 is the only data element
  to be stored, it can be stored as trie8. Assume
  now that another string identified as 8453 is
  added. To make room for the second element, we
  allocate another 10-element array and have
  trie8 point to it. We push 8376 down and now is
  indexed as trie83, while the new element,
  8453 will be stored under trie84.

3
Patricia (PAT) Trees

• Basic definition A trie with the additional
  constraint that single-descendant nodes are
  eliminated.
• Example
• PAT arrays provide the same functionality as PAT
  trees with less space requirement.

4
Suffix Trees

• Basic definition A trie data structure (usually
  a Patricia tree) built over all suffixes of a
  text
• Example
• A suffix tree for a text of n characters can be
  built in O(n) time.
• Suffix arrays provide the same functionality as
  suffix trees with less space requirement. See
  page 200 of your text for more on suffix arrays.

5
IR using Suffix Trees

• Text is view as one long string and each position
  in the text corresponds to a semi-infinite
  string.
• No keywords or terms are used. Queries are based
  on substrings of the text.
• The text does not need structure, but if there is
  one, it can be used.
• Searches supported
• Proximity searching
• Range searching
• Regular expression searching