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34
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 172 (78 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.
Simple linear work suffix array construction
, 2003
"... Abstract. Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to lineartime construction algorithms and more exp ..."
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Cited by 149 (6 self)
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Abstract. Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to lineartime construction algorithms and more explicit structure. We narrow this gap between theory and practice with a simple lineartime construction algorithm for suffix arrays. The simplicity is demonstrated with a C++ implementation of 50 effective lines of code. The algorithm is called DC3, which stems from the central underlying concept of difference cover. This view leads to a generalized algorithm, DC, that allows a spaceefficient implementation and, moreover, supports the choice of a space–time tradeoff. For any v ∈ [1, √ n], it runs in O(vn) time using O(n / √ v) space in addition to the input string and the suffix array. We also present variants of the algorithm for several parallel and hierarchical memory models of computation. The algorithms for BSP and EREWPRAM models are asymptotically faster than all previous suffix tree or array construction algorithms.
Space efficient linear time construction of suffix arrays
 Journal of Discrete Algorithms
, 2003
"... Abstract. We present a linear time algorithm to sort all the suffixes of a string over a large alphabet of integers. The sorted order of suffixes of a string is also called suffix array, a data structure introduced by Manber and Myers that has numerous applications in pattern matching, string proces ..."
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Cited by 72 (1 self)
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Abstract. We present a linear time algorithm to sort all the suffixes of a string over a large alphabet of integers. The sorted order of suffixes of a string is also called suffix array, a data structure introduced by Manber and Myers that has numerous applications in pattern matching, string processing, and computational biology. Though the suffix tree of a string can be constructed in linear time and the sorted order of suffixes derived from it, a direct algorithm for suffix sorting is of great interest due to the space requirements of suffix trees. Our result improves upon the best known direct algorithm for suffix sorting, which takes O(n log n) time. We also show how to construct suffix trees in linear time from our suffix sorting result. Apart from being simple and applicable for alphabets not necessarily of fixed size, this method of constructing suffix trees is more space efficient. 1
Engineering a lightweight suffix array construction algorithm (Extended Abstract)
"... In this paper we consider the problem of computing the suffix array of a text T [1, n]. This problem consists in sorting the suffixes of T in lexicographic order. The suffix array [16] (or pat array [9]) is a simple, easy to code, and elegant data structure used for several fundamental string matchi ..."
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Cited by 59 (4 self)
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In this paper we consider the problem of computing the suffix array of a text T [1, n]. This problem consists in sorting the suffixes of T in lexicographic order. The suffix array [16] (or pat array [9]) is a simple, easy to code, and elegant data structure used for several fundamental string matching problems involving both linguistic texts and biological data [4, 11]. Recently, the interest in this data structure has been revitalized by its use as a building block for three novel applications: (1) the BurrowsWheeler compression algorithm [3], which is a provably [17] and practically [20] effective compression tool; (2) the construction of succinct [10, 19] and compressed [7, 8] indexes; the latter can store both the input text and its fulltext index using roughly the same space used by traditional compressors for the text alone; and (3) algorithms for clustering and ranking the answers to user queries in websearch engines [22]. In all these applications the construction of the suffix array is the computational bottleneck both in time and space. This motivated our interest in designing yet another suffix array construction algorithm which is fast and "lightweight" in the sense that it uses small space...
The enhanced suffix array and its applications to genome analysis
 In Proc. Workshop on Algorithms in Bioinformatics, in Lecture Notes in Computer Science
, 2002
"... Abstract. In large scale applications as computational genome analysis, the space requirement of the suffix tree is a severe drawback. In this paper, we present a uniform framework that enables us to systematically replace every string processing algorithm that is based on a bottomup traversal of a ..."
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Cited by 43 (5 self)
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Abstract. In large scale applications as computational genome analysis, the space requirement of the suffix tree is a severe drawback. In this paper, we present a uniform framework that enables us to systematically replace every string processing algorithm that is based on a bottomup traversal of a suffix tree by a corresponding algorithm based on an enhanced suffix array (a suffix array enhanced with the lcptable). In this framework, we will show how maximal, supermaximal, and tandem repeats, as well as maximal unique matches can be efficiently computed. Because enhanced suffix arrays require much less space than suffix trees, very large genomes can now be indexed and analyzed, a task which was not feasible before. Experimental results demonstrate that our programs require not only less space but also much less time than other programs developed for the same tasks. 1
A taxonomy of suffix array construction algorithms
 ACM Computing Surveys
, 2007
"... In 1990, Manber and Myers proposed suffix arrays as a spacesaving alternative to suffix trees and described the first algorithms for suffix array construction and use. Since that time, and especially in the last few years, suffix array construction algorithms have proliferated in bewildering abunda ..."
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Cited by 39 (10 self)
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In 1990, Manber and Myers proposed suffix arrays as a spacesaving alternative to suffix trees and described the first algorithms for suffix array construction and use. Since that time, and especially in the last few years, suffix array construction algorithms have proliferated in bewildering abundance. This survey paper attempts to provide simple highlevel descriptions of these numerous algorithms that highlight both their distinctive features and their commonalities, while avoiding as much as possible the complexities of implementation details. New hybrid algorithms are also described. We provide comparisons of the algorithms ’ worstcase time complexity and use of additional space, together with results of recent experimental test runs on many of their implementations.
Optimal Exact String Matching Based on Suffix Arrays
 In Proceedings of the Ninth International Symposium on String Processing and Information Retrieval. SpringerVerlag, Lecture Notes in Computer Science
, 2002
"... Using the suffix tree of a string S, decision queries of the type "Is P a substring of S?" can be answered in O(P) time and enumeration queries of the type "Where are all z occurrences of P in S?" can be answered in O(P+z) time, totally independent of the size of S. However, in large scale appli ..."
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Cited by 37 (1 self)
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Using the suffix tree of a string S, decision queries of the type "Is P a substring of S?" can be answered in O(P) time and enumeration queries of the type "Where are all z occurrences of P in S?" can be answered in O(P+z) time, totally independent of the size of S. However, in large scale applications as genome analysis, the space requirements of the suffix tree are a severe drawback. The suffix array is a more space economical index structure. Using it and an additional table, Manber and Myers (1993) showed that decision queries and enumeration queries can be answered in O(P+log S) and O(P+log S+z) time, respectively, but no optimal time algorithms are known. In this paper, we showhow to achieve the optimal O(P) and O(P+z) time bounds for the suffix array. Our approach is not confined to exact pattern matching. In fact, it can be used to efficiently solve all problems that are usually solved bya topdown traversal of the suffix tree. Experiments show that our method is not only of theoretical interest but also of practical relevance.
Detecting higherlevel similarity patterns in programs
 In ESEC/FSE
, 2005
"... Cloning in software systems is known to create problems during software maintenance. Several techniques have been proposed to detect the same or similar code fragments in software, socalled simple clones. While the knowledge of simple clones is useful, detecting designlevel similarities in softwar ..."
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Cited by 34 (7 self)
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Cloning in software systems is known to create problems during software maintenance. Several techniques have been proposed to detect the same or similar code fragments in software, socalled simple clones. While the knowledge of simple clones is useful, detecting designlevel similarities in software could ease maintenance even further, and also help us identify reuse opportunities. We observed that recurring patterns of simple clones – socalled structural clones often indicate the presence of interesting designlevel similarities. An example would be patterns of collaborating classes or components. Finding structural clones that signify potentially useful design information requires efficient techniques to analyze the bulk of simple clone data and making nontrivial inferences based on the abstracted information. In this paper, we describe a practical solution to the problem of
Two space saving tricks for linear time LCP computation
, 2004
"... Abstract. In this paper we consider the linear time algorithm of Kasai et al. [6] for the computation of the Longest Common Prefix (LCP) array given the text and the suffix array. We show that this algorithm can be implemented without any auxiliary array in addition to the ones required for the inpu ..."
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Cited by 31 (3 self)
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Abstract. In this paper we consider the linear time algorithm of Kasai et al. [6] for the computation of the Longest Common Prefix (LCP) array given the text and the suffix array. We show that this algorithm can be implemented without any auxiliary array in addition to the ones required for the input (the text and the suffix array) and the output (the LCP array). Thus, for a text of length n, we reduce the space occupancy of this algorithm from 13n bytes to 9n bytes. We also consider the problem of computing the LCP array by “overwriting” the suffix array. For this problem we propose an algorithm whose space occupancy can be bounded in terms of the empirical entropy of the input text. Experiments show that for linguistic texts our algorithm uses roughly 7n bytes. Our algorithm makes use of the BurrowsWheeler Transform even if it does not represent any data in compressed form. To our knowledge this is the first application of the BurrowsWheeler Transform outside the domain of data compression. The source code for the algorithms described in this paper has been included in the lightweight suffix sorting package [13] which is freely available under the GNU GPL. 1
Fast lightweight suffix array construction and checking
 14th Annual Symposium on Combinatorial Pattern Matching
, 2003
"... We describe an algorithm that, for any v 2 [2; n], constructs the suffix array of a string of length n in O(vn + n log n) time using O(v + n= p v) space in addition to the input (the string) and the output (the suffix array). By setting v = log n, we obtain an O(n log n) time algorithm using O n= p ..."
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Cited by 25 (5 self)
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We describe an algorithm that, for any v 2 [2; n], constructs the suffix array of a string of length n in O(vn + n log n) time using O(v + n= p v) space in addition to the input (the string) and the output (the suffix array). By setting v = log n, we obtain an O(n log n) time algorithm using O n= p