Suffix Tree

Synonyms

Compact suffix tries

Definition

The suffix tree ${\cal S}(y)$ of a non-empty string y of length n is a compact trie representing all the suffixes of the string.

The suffix tree of y is defined by the following properties:

• 1. All branches of ${\cal S}(y)$ are labeled by all nonempty suffixes of y _⊔.

• 2. Edges of ${\cal S}(y)$ are labeled by strings.

• 3. Internal nodes of ${\cal S}(y)$ have at least two children.

• 4. Edges outgoing an internal node are labeled by segments starting with different letters.

• 5. The segments are represented both by their starting position on y and their lengths.

The space sign _⊔ appended at the end of y avoids marking nodes, and implies that ${\cal S}(y)$ has exactly n leaves (number of non-empty suffixes).

All the properties then imply that the total size of ${\cal S}(y)$ is O(n), which makes it possible to design a linear-time construction of the suffix tree.

Historical Background

The first linear time algorithm for building a suffix tree...