NDLI: Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching

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Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vitter, Jeffrey Scott Grossi, Roberto
Copyright Year	2005
Abstract	The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for space-efficient text indexing methods that support fast string searching. We model this scenario as follows: Consider a text T consisting of n symbols drawn from a fixed alphabet $\Sigma$. The text T can be represented in $n \lg \|\Sigma\|$ bits by encoding each symbol with $\lg \|\Sigma\|$ bits. The goal is to support fast online queries for searching any string pattern P of m symbols, with T being fully scanned only once, namely, when the index is created at preprocessing time. The text indexing schemes published in the literature are greedy in terms of space usage: they require $\Omega(n \lg n)$ additional bits of space in the worst case. For example, in the standard unit cost RAM, suffix trees and suffix arrays need $\Omega(n)$ memory words, each of $\Omega(\lg n)$ bits. These indexes are larger than the text itself by a multiplicative factor of $\Omega(\smash{\lg_{\|\Sigma\|} n})$, which is significant when $\Sigma$ is of constant size, such as in \textsc{ascii} or \textsc{unicode}. On the other hand, these indexes support fast searching, either in $O(m \lg \|\Sigma\|)$ time or in $O(m +\lg n)$ time, plus an output-sensitive cost $O(\mathit{occ})$ for listing the $\mathit{occ}$ pattern occurrences. We present a new text index that is based upon compressed representations of suffix arrays and suffix trees. It achieves a fast $\smash{O(m /\lg_{\|\Sigma\|} n + \lg_{\|\Sigma\|}^\epsilon n)}$ search time in the worst case, for any constant $0 < \epsilon \leq 1$, using at most $\smash{\bigl(\epsilon^{-1} + O(1)\bigr) \, n \lg \|\Sigma\|}$ bits of storage. Our result thus presents for the first time an efficient index whose size is provably linear in the size of the text in the worst case, and for many scenarios, the space is actually sublinear in practice. As a concrete example, the compressed suffix array for a typical 100 MB \textsc{ascii} file can require 30--40 MB or less, while the raw suffix array requires 500 MB. Our theoretical bounds improve \emph{both} time and space of previous indexing schemes. Listing the pattern occurrences introduces a sublogarithmic slowdown factor in the output-sensitive cost, giving $O(\mathit{occ} \, \smash{\lg_{\|\Sigma\|}^\epsilon n})$ time as a result. When the patterns are sufficiently long, we can use auxiliary data structures in $O(n \lg \|\Sigma\|)$ bits to obtain a total search bound of $O(m /\lg_{\|\Sigma\|} n + \mathit{occ})$ time, which is optimal.
Starting Page	378
Ending Page	407
Page Count	30
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539702402354
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Coding and information theory pattern matching text retrieval Data structures text indexing Nonnumerical algorithms suffix trees Analysis of algorithms and problem complexity string searching Searching and sorting compressed data structures compression suffix arrays
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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