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Compressed suffix arrays and suffix trees with applications to text indexing and string matching
, 2005
"... The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for spaceefficient 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 Σ. ..."
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Cited by 192 (17 self)
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The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for spaceefficient 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 Σ. The text T can be represented in n lg Σ  bits by encoding each symbol with lg Σ  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 Ω(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 Ω(n) memory words, each of Ω(lg n) bits. These indexes are larger than the text itself by a multiplicative factor of Ω(lg Σ  n), which is significant when Σ is of constant size, such as in ascii or unicode. On the other hand, these indexes support fast searching, either in O(m lg Σ) timeorinO(m +lgn) time, plus an outputsensitive cost O(occ) for listing the 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 O(m / lg Σ  n +lgɛ Σ  n) search time in the worst case, for any constant
Opportunistic Data Structures with Applications
, 2000
"... In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space ..."
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Cited by 189 (11 self)
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In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space reduction is achieved at no significant slowdown in the query performance. More precisely, its space occupancy is optimal in an informationcontent sense because a text T [1, u] is stored using O(H k (T )) + o(1) bits per input symbol in the worst case, where H k (T ) is the kth order empirical entropy of T (the bound holds for any fixed k). Given an arbitrary string P [1; p], the opportunistic data structure allows to search for the occ occurrences of P in T in O(p + occ log u) time (for any fixed > 0). If data are uncompressible we achieve the best space bound currently known [12]; on compressible data our solution improves the succinct suffix array of [12] and the classical suffix tree and suffix array data structures either in space or in query time or both.
Compressed fulltext indexes
 ACM COMPUTING SURVEYS
, 2007
"... Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text l ..."
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Cited by 180 (81 self)
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Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text length. This concept has evolved into selfindexes, which in addition contain enough information to reproduce any text portion, so they replace the text. The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising results in a very short time, and radically changed the status of this area in less than five years. The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously. In this paper we present the main concepts underlying selfindexes. We explain the relationship between text entropy and regularities that show up in index structures and permit compressing them. Then we cover the most relevant selfindexes up to date, focusing on the essential aspects on how they exploit the text compressibility and how they solve efficiently various search problems. We aim at giving the theoretical background to understand and follow the developments in this area.
Indexing Text using the ZivLempel Trie
 Journal of Discrete Algorithms
, 2002
"... Let a text of u characters over an alphabet of size be compressible to n symbols by the LZ78 or LZW algorithm. We show that it is possible to build a data structure based on the ZivLempel trie that takes 4n log 2 n(1+o(1)) bits of space and reports the R occurrences of a pattern of length m in ..."
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Cited by 66 (43 self)
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Let a text of u characters over an alphabet of size be compressible to n symbols by the LZ78 or LZW algorithm. We show that it is possible to build a data structure based on the ZivLempel trie that takes 4n log 2 n(1+o(1)) bits of space and reports the R occurrences of a pattern of length m in worst case time O(m log(m)+(m+R)log n).
A Subquadratic Sequence Alignment Algorithm for Unrestricted Cost Matrices
, 2002
"... The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring ..."
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Cited by 60 (4 self)
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The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring matrix of unrestricted weights. Our algorithm applies to both local and global alignment computations. The speedup is achieved by dividing the dynamic programming matrix into variable sized blocks, as induced by LempelZiv parsing of both strings, and utilizing the inherent periodic nature of both strings. This leads to an O(n 2 = log n) algorithm for an input of constant alphabet size. For most texts, the time complexity is actually O(hn 2 = log n) where h 1 is the entropy of the text. Institut GaspardMonge, Universite de MarnelaVallee, Cite Descartes, ChampssurMarne, 77454 MarnelaVallee Cedex 2, France, email: mac@univmlv.fr. y Department of Computer Science, Haifa University, Haifa 31905, Israel, phone: (9724) 8240103, FAX: (9724) 8249331; Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY 112013840; email: landau@poly.edu; partially supported by NSF grant CCR0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation (grants 173/98 and 282/01), by the FIRST Foundation of the Israel Academy of Science and Humanities, and by IBM Faculty Partnership Award. z Department of Computer Science, Haifa University, Haifa 31905, Israel; On Education Leave from the IBM T.J.W. Research Center; email: michal@cs.haifa.il; partially supported by by the Israel Science Foundation (grants 173/98 and 282/01), and by the FIRST Foundation of the Israel Academy of Science ...
A Practical qGram Index for Text Retrieval Allowing Errors
 CLEI Electronic Journal
, 1998
"... We propose an indexing technique for approximate text searching, which is practical and powerful, and especially optimized for natural language text. Unlike other indices of this kind, it is able to retrieve any string that approximately matches the search pattern, not only words. Every text substri ..."
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Cited by 33 (9 self)
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We propose an indexing technique for approximate text searching, which is practical and powerful, and especially optimized for natural language text. Unlike other indices of this kind, it is able to retrieve any string that approximately matches the search pattern, not only words. Every text substring of a fixed length q is stored in the index, together with pointers to all the text positions where it appears. The search pattern is partitioned into pieces which are searched in the index, and all their occurrences in the text are verified for a complete match. To reduce space requirements, pointers to blocks instead of exact positions can be used, which increases querying costs. We design an algorithm to optimize the pattern partition into pieces so that the total number of verifications is minimized. This is especially well suited for natural language texts, and allows to know in advance the expected cost of the search and the expected relevance of the query to the user. We show experi...
Approximate Text Searching
, 1998
"... This thesis focuses on the problem of text retrieval allowing errors, also called \approximate " string matching. The problem is to nd a pattern in a text, where the pattern and the text may have \errors". This problem has received a lot of attention in recent years because of its applicat ..."
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Cited by 22 (6 self)
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This thesis focuses on the problem of text retrieval allowing errors, also called \approximate " string matching. The problem is to nd a pattern in a text, where the pattern and the text may have \errors". This problem has received a lot of attention in recent years because of its applications in many areas, such as information retrieval, computational biology and signal processing, to name a few. The aim of this work is the development and analysis of novel algorithms to deal with the problem under various conditions, as well as a better understanding of the problem itself and its statistical behavior. Although our results are valid in many dierent areas, we focus our attention on typical text searching for information retrieval applications. This makes some ranges of values for the parameters of the problem more interesting than others. We have divided this presentation in two parts. The rst one deals with online approximate string matching, i.e. when there is no time or space to preprocess the text. These algorithms are the core of oline algorithms as well. Online searching is the area of the problem where better algorithms existed. We have obtained new bounds for the probability of an approximate match of a pattern in
Fullycompressed suffix trees
 IN: PACS 2000. LNCS
, 2000
"... Suffix trees are by far the most important data structure in stringology, with myriads of applications in fields like bioinformatics and information retrieval. Classical representations of suffix trees require O(n log n) bits of space, for a string of size n. This is considerably more than the nlog ..."
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Cited by 21 (15 self)
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Suffix trees are by far the most important data structure in stringology, with myriads of applications in fields like bioinformatics and information retrieval. Classical representations of suffix trees require O(n log n) bits of space, for a string of size n. This is considerably more than the nlog 2 σ bits needed for the string itself, where σ is the alphabet size. The size of suffix trees has been a barrier to their wider adoption in practice. Recent compressed suffix tree representations require just the space of the compressed string plus Θ(n) extra bits. This is already spectacular, but still unsatisfactory when σ is small as in DNA sequences. In this paper we introduce the first compressed suffix tree representation that breaks this linearspace barrier. Our representation requires sublinear extra space and supports a large set of navigational operations in logarithmic time. An essential ingredient of our representation is the lowest common ancestor (LCA) query. We reveal important connections between LCA queries and suffix tree navigation.
A compressed selfindex using a ZivLempel dictionary
 In: SPIRE. Volume 4209 of LNCS. (2006) 163–180
"... Abstract. A compressed fulltext selfindex for a text T, of size u, is a data structure used to search patterns P, of size m, in T that requires reduced space, i.e. that depends on the empirical entropy (Hk, H0) of T, and is, furthermore, able to reproduce any substring of T. In this paper we prese ..."
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Cited by 19 (6 self)
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Abstract. A compressed fulltext selfindex for a text T, of size u, is a data structure used to search patterns P, of size m, in T that requires reduced space, i.e. that depends on the empirical entropy (Hk, H0) of T, and is, furthermore, able to reproduce any substring of T. In this paper we present a new compressed selfindex able to locate the occurrences of P in O((m + occ) log n) time, where occ is the number of occurrences and σ the size of the alphabet of T. The fundamental improvement over previous LZ78 based indexes is the reduction of the search time dependency on m from O(m 2) to O(m). To achieve this result we point out the main obstacle to linear time algorithms based on LZ78 data compression and expose and explore the nature of a recurrent structure in LZindexes, the T78 suffix tree. We show that our method is very competitive in practice by comparing it against the LZIndex, the FMindex and a compressed suffix array. 1
LempelZiv Index for qGrams
, 1998
"... . We present a new sublinearsize index structure for finding all occurrences of a given qgram in a text. Such a qgram index is needed in many approximate pattern matching algorithms. All earlier qgram indexes require at least O(n) space, where n is the length of the text. The new LempelZiv in ..."
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Cited by 18 (2 self)
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. We present a new sublinearsize index structure for finding all occurrences of a given qgram in a text. Such a qgram index is needed in many approximate pattern matching algorithms. All earlier qgram indexes require at least O(n) space, where n is the length of the text. The new LempelZiv index needs only O(n/log n) space while being as fast as previous methods. The new method takes advantage of repetitions in the text found by LempelZiv parsing. Key Words. qGram index, Approximate pattern matching, Text indexing, LempelZiv parsing, String algorithms, Data compression. 1. Introduction. The approximate pattern matching problem is as follows. Given a text T = T [1, n] and a pattern P = P[1, m] in an alphabet # and an integer k, find all the text positions i such that an approximate occurrence of P with at most k differences ends at i . The difference between two strings # and # is measured as the edit distance d: d(#, #) is the minimum number of edit operations (in...