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.
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 trie[8]. 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 trie[8] point to
it. We push 8376 down and now is indexed as
trie[8][3], while the new element, 8453 will be
stored under trie[8][4].
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.
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.
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