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13
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...
A Hybrid Indexing Method for Approximate String Matching
"... We present a new indexing method for the approximate string matching problem. The method is based on a suffix array combined with a partitioning of the pattern. We analyze the resulting algorithm and show that the average retrieval time is Ç Ò � ÐÓ � Ò,forsome�� that depends on the error fraction t ..."
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Cited by 56 (10 self)
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We present a new indexing method for the approximate string matching problem. The method is based on a suffix array combined with a partitioning of the pattern. We analyze the resulting algorithm and show that the average retrieval time is Ç Ò � ÐÓ � Ò,forsome�� that depends on the error fraction tolerated « and the alphabet size �. Itisshownthat �� for approximately « � � � Ô �,where � � � � ����. Thespace required is four times the text size, which is quite moderate for this problem. We experimentally show that this index can outperform by far all the existing alternatives for indexed approximate searching. These are also the first experiments that compare the different existing schemes.
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.
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
Faster Lightweight Suffix Array Construction
"... The suffix array is a data structure formed by sorting the suffixes of a string into lexicographical order. It is important for a variety of applications, perhaps most notably pattern matching, pattern discovery and blocksorting data compression. The last decade has seen intensive research toward e ..."
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Cited by 10 (3 self)
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The suffix array is a data structure formed by sorting the suffixes of a string into lexicographical order. It is important for a variety of applications, perhaps most notably pattern matching, pattern discovery and blocksorting data compression. The last decade has seen intensive research toward efficient construction of suffix arrays with algorithms striving not only to be fast, but also “lightweight” (in the sense that they use small working memory). In this paper we describe a new lightweight suffix array construction algorithm. By exploiting several interesting properties of suffixes in combination with cache concious programming we acheive excellent runtimes. Extensive experiments show our approach to be faster that all other known algorithms for the task.
Unifying Text Search And Compression  Suffix Sorting, Block Sorting and Suffix Arrays
, 2000
"... Today many electronic documents are available such as articles of newspapers, dictionaries, books, DNA sequences, etc. and they are stored in databases. We also have many documents on the Internet and have many email documents. Therefore, fast queries on such huge amount of documents and their comp ..."
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Cited by 6 (0 self)
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Today many electronic documents are available such as articles of newspapers, dictionaries, books, DNA sequences, etc. and they are stored in databases. We also have many documents on the Internet and have many email documents. Therefore, fast queries on such huge amount of documents and their compression to reduce costs for storing or transferring them are important. In this thesis, a unified method for improving efficiency of search and compression for huge text data is proposed. All search methods and compression methods used in this thesis are related to a data structure called suffix array. The suffix array is a text search data structure and it is used in a text compression method called block sorting. Both are promising search method and compression method and there are many studies on the methods. Now a data structure called inverted file is used for queries from huge amount of documents. Though it is widely used, query unit is a document in order to reduce disk space to sto...
Reconstructing a Suffix Array
"... Abstract. For certain problems (for example, computing repetitions and repeats, data compression applications) it is not necessary that the suffixes of a string represented in a suffix tree or suffix array should occur in lexicographical order (lexorder). It thus becomes of interest to study possibl ..."
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Cited by 2 (0 self)
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Abstract. For certain problems (for example, computing repetitions and repeats, data compression applications) it is not necessary that the suffixes of a string represented in a suffix tree or suffix array should occur in lexicographical order (lexorder). It thus becomes of interest to study possible alternate orderings of the suffixes in these data structures, that may be easier to construct or more efficient to use. In this paper we consider the “reconstruction ” of a suffix array based on a given reordering of the alphabet, and we describe simple timeand spaceefficient algorithms that accomplish it.
Direct Suffix Sorting and its Applications
, 2008
"... The suffix sorting problem is to construct the suffix array for an input sequence. Given a sequence T[0...n − 1] of size n = T , with symbols from a fixed alphabet Σ, (Σ  ≤ n), the suffix array provides a compact representation of all the suffixes of T in a lexicographic order. Traditionally, t ..."
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The suffix sorting problem is to construct the suffix array for an input sequence. Given a sequence T[0...n − 1] of size n = T , with symbols from a fixed alphabet Σ, (Σ  ≤ n), the suffix array provides a compact representation of all the suffixes of T in a lexicographic order. Traditionally, the suffix array is often constructed by first building the suffix tree for T, and then performing an inorder traversal of the suffix tree. The direct suffix sorting problem is to construct the suffix array of T directly without using the suffix tree data structure. We propose a direct suffix sorting algorithm which rearranges the biological sequences of interests and facilitates high throughput pattern query, retrieval and storage in O(n) time. The improved algorithm requires only 7n bytes of storage, including the n bytes for the original string, and the 4n bytes for the suffix array. The basis of our improved algorithm is an extension of ShannonFanoElias codes used in information theory. This is the first time informationtheoretic methods have been used as the basis for solving the suffix sorting problem. The direct suffix sorting algorithm is then applied to solve the multiple sequence alignment problem. The sequences to be aligned are concatenated and then passed to
STRING DATA STRUCTURES FOR COMPUTATIONAL MOLECULAR BIOLOGY
"... The topic of the chapter is string data structures with applications in the field of computational molecular biology. Let � be a finite alphabet consisting of a set of characters (or symbols). The cardinality of the alphabet denoted by �  expresses the number of distinct characters in the alphabet ..."
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The topic of the chapter is string data structures with applications in the field of computational molecular biology. Let � be a finite alphabet consisting of a set of characters (or symbols). The cardinality of the alphabet denoted by �  expresses the number of distinct characters in the alphabet. A string or word is an ordered list