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  or from the shortest to the longest suffix. 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.
- Ukkonen, E. (1995). "On-line construction of suffix trees". Algorithmica 14 (3): 249–260. doi:10.1007/BF01206331.
- McCreight, E. M. (1976). "A Space-Economical Suffix Tree Construction Algorithm". Journal of the ACM 23 (2): 262. doi:10.1145/321941.321946.
- Weiner, P. (1973). "14th Annual Symposium on Switching and Automata Theory (swat 1973)". pp. 1–9. doi:10.1109/SWAT.1973.13.
- Original Ukkonen's paper PDF | PDF with figures
- McCreight's paper in PDF
- Weiner's paper in PDF
- Detailed explanation in plain English
- Fast String Searching With Suffix Trees Mark Nelson's tutorial. Has an implementation example written with C++.
- Implementation in C with detailed explanation
- Lecture slides by Guy Blelloch
- Ukkonen's homepage
- Text-Indexing project (Ukkonen's linear-time construction of suffix trees)
- Implementation in C Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
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