Suffix Tree - Definition

Definition

The suffix tree for the string of length is defined as a tree such that:

  • the paths from the root to the leaves have a one-to-one relationship with the suffixes of ,
  • edges spell non-empty strings,
  • and all internal nodes (except perhaps the root) have at least two children.

Since such a tree does not exist for all strings, is padded with a terminal symbol not seen in the string (usually denoted $). This ensures that no suffix is a prefix of another, and that there will be leaf nodes, one for each of the suffixes of . Since all internal non-root nodes are branching, there can be at most n − 1 such nodes, and n + (n − 1) + 1 = 2n nodes in total (n leaves, n − 1 internal nodes, 1 root).

Suffix links are a key feature for older linear-time construction algorithms, although most newer algorithms, which are based on Farach's algorithm, dispense with suffix links. In a complete suffix tree, all internal non-root nodes have a suffix link to another internal node. If the path from the root to a node spells the string, where is a single character and is a string (possibly empty), it has a suffix link to the internal node representing . See for example the suffix link from the node for ANA to the node for NA in the figure above. Suffix links are also used in some algorithms running on the tree.

Read more about this topic:  Suffix Tree

Famous quotes containing the word definition:

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.”
    Jane Adams (20th century)