NDLI: On the sorting-complexity of suffix tree construction

Content Provider	ACM Digital Library
Author	Farach-Colton, Martin Ferragina, Paolo Muthukrishnan, S.
Copyright Year	2000
Abstract	The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. We present a recursive technique for building suffix trees that yields optimal algorithms in different computational models. Sorting is an inherent bottleneck in building suffix trees and our algorithms match the sorting lower bound. Specifically, we present the following results. (1) Weiner [1973], who introduced the data structure, gave an optimal $\textit{0}(\textit{n})-time$ algorithm for building the suffix tree of an $\textit{n}-character$ string drawn from a constant-size alphabet. In the comparison model, there is a trivial $&Ogr;(\textit{n}$ log $\textit{n})-time$ lower bound based on sorting, and Weiner's algorithm matches this bound. For integer alphabets, the fastest known algorithm is the $\textit{O}(\textit{n}$ log $\textit{n})time$ comparison-based algorithm, but no super-linear lower bound is known. Closing this gap is the main open question in stringology. We settle this open problem by giving a linear time reduction to sorting for building suffix trees. Since sorting is a lower-bound for building suffix trees, this algorithm is time-optimal in every alphabet mode. In particular, for an alphabet consisting of integers in a polynomial range we get the first known linear-time algorithm. (2) All previously known algorithms for building suffix trees exhibit a marked absence of locality of reference, and thus they tend to elicit many page faults (I/Os) when indexing very long strings. They are therefore unsuitable for building suffix trees in secondary storage devices, where I/Os dominate the overall computational cost. We give a linear-I/O reduction to sorting for suffix tree construction. Since sorting is a trivial I/O-lower bound for building suffix trees, our algorithm is I/O-optimal.
Starting Page	987
Ending Page	1011
Page Count	25
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/355541.355547
Journal	Journal of the ACM (JACM)
Volume Number	47
Issue Number	6
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2000-11-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	DAM model RAM model External-memory data structures Sorting complexity Suffix array Suffix tree
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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