Suffix Trees: A Fast Data Structure for String Operations - Prof. Fawzi Philip Emad, Study notes of Computer Science

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Suffix Trees

Suffix trees

• A data structure used to allow for very fast string operations
• After preparing a base text of size n
• Can search for a query string of size k in time k
• Can also do other things, such as find repeated strings and palindromes

Suffix tree for abbab$

a b $ b b $ a b $ a b $ b $ a b $

That $ character

• String is appended with a unique character (typically $)
• Ensures that no String is a prefix of any other
• Ensures that each suffix ends in a leaf
  • makes a number of the algorithms simpler

Compressed Suffix trees

• No internal node has only one child
• Internal nodes are labeled with the prefix of all strings beneath them
• From an internal node n , the edge labeled c gives the tree with all strings consisting of the common prefix followed by c

Building Suffix trees

• There are fancy algorithms for building suffix trees that require only O( n ) time to build a suffix tree for a string consisting of n characters. - we won’t be using one of those
• Simply insert suffixes one at a time, inserting new internal nodes as needed - not too bad in practice

Useful data

• Each node needs to store:
  • common prefix (String)
  • pointers to children
    • use an array
• Useful to store
  • total number of suffixes stored in this tree

What will we be doing

• Find the length of the maximum repeated String
• Find all strings with a minimum length and a minimum frequency - can leave out Strings that are prefixes of other answers
• Find all suffixes that start with a given String

Implementation

• Only the methods of SuffixTree will be tested - you can implement it however you like, so long as you are actually building a suffix tree - as opposed to, for example, storing stuff as a String and just using very expensive algorithms

Implementation Suggestion

• An interface is provided
  • Node
• You write subclasses
• For example, EmptyNode and NonEmptyNode

Performance measurement

• You are asked not to directly compare strings
• instead, use the SuffixTree. lengthCommonPrefix method, which records the number of characters compared