# Ukkonen's algorithm

In computer science, Ukkonen's algorithm is a linear-time, online algorithm for constructing suffix trees, proposed by Esko Ukkonen in 1995.[1]

The algorithm begins with an implicit suffix tree containing the first character of the string. Then it steps through the string adding successive characters until the tree is complete. This order addition of characters gives Ukkonen's algorithm its "on-line" property. Earlier algorithms proceeded backward from the last character to the first one, let it be from the longest to the shortest suffix [2] or from the shortest to the longest suffix.[3] The naive implementation for generating a suffix tree requires O(n2) or even O(n3) time, where n is the length of the string. By exploiting a number of algorithmic techniques, Ukkonen reduced this to O(n) (linear) time, for constant-size alphabets, and O(n log n) in general.

## References

1. ^ Ukkonen, E. (1995). "On-line construction of suffix trees". Algorithmica 14 (3): 249–260. doi:10.1007/BF01206331. edit
2. ^ McCreight, E. M. (1976). "A Space-Economical Suffix Tree Construction Algorithm". Journal of the ACM 23 (2): 262. doi:10.1145/321941.321946. edit
3. ^ Weiner, P. (1973). "Linear pattern matching algorithms". 14th Annual Symposium on Switching and Automata Theory (swat 1973). pp. 1–9. doi:10.1109/SWAT.1973.13. edit