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.

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