From Ukkonen to Mccreight and Weiner: a Unifying View of Linear-time Suux Tree Construction

We review the linear time suux tree constructions by Weiner, McCreight, and Ukkonen. We use the terminology of the most recent algorithm, Ukkonen's online construction, to explain its historic predecessors. This reveals relationships much closer than one would expect, since the three algorithms are based on rather diierent intuitive ideas. Moreover, it completely explains the diierences between these algorithms in terms of simplicity, eeciency, and implementation complexity. 1 Motivation and Overview Suux trees provide most eecient solutions to a \myriad" 4] of string processing problems. The suux tree for a string t really turns t inside out, immediately exposing properties like longest or most frequent subwords. The fundamental question whether w occurs in t can be answered in O(jwj) steps | independent of the length of t | once the suux tree for t is constructed. Thus it is of great importance that the suux tree for t can be constructed and represented in linear time and space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention suux trees, and never give eecient algorithms for their construction 3, 21, 11, 1, 17, 7]. Recent exceptions are 22, 13]. The reason for this is historical: starting with the seminal paper by Weiner 26], suux tree construction has built up a reputation of being overly complicated. The purpose of the present paper is to correct this reputation | by working out what is essential about eecient suux tree construction, and what is unnecessary complexity.