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:
“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 (17721834)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than thisdevoted and obedient. This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (18201910)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (18391894)