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Suffix arrays: A new method for online string searches
 SIAM J. Comput
, 1993
"... Abstract. A new and conceptually simple data structure, called a suffix array, for online string searches is introduced in this paper. Constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms. The main advantage of suffix arrays over suffix tree ..."
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Cited by 649 (1 self)
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Abstract. A new and conceptually simple data structure, called a suffix array, for online string searches is introduced in this paper. Constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms. The main advantage of suffix arrays over suffix trees is that, in practice, they use three to five times less space. From a complexity standpoint, suffix arrays permit online string searches of the type, "Is W a substring of A? " to be answered in time O(P + log N), where P is the length of W and N is the length of A, which is competitive with (and in some cases slightly better than) suffix trees. The only drawback is that in those instances where the underlying alphabet is finite and small, suffix trees can be constructed in O (N) time in the worst case, versus O (N log N) time for suffix arrays. However, an augmented algorithm is given that, regardless of the alphabet size, constructs suffix arrays in O (N) expected time, albeit with lesser.space efficiency. It is believed that suffix arrays will prove to be better in practice than suffix trees for many applications.
A blocksorting lossless data compression algorithm
, 1994
"... The charter of SRC is to advance both the state of knowledge and the state of the art in computer systems. From our establishment in 1984, we have performed basic and applied research to support Digital’s business objectives. Our current work includes exploring distributed personal computing on mult ..."
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Cited by 571 (5 self)
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The charter of SRC is to advance both the state of knowledge and the state of the art in computer systems. From our establishment in 1984, we have performed basic and applied research to support Digital’s business objectives. Our current work includes exploring distributed personal computing on multiple platforms, networking, programming technology, system modelling and management techniques, and selected applications. Our strategy is to test the technical and practical value of our ideas by building hardware and software prototypes and using them as daily tools. Interesting systems are too complex to be evaluated solely in the abstract; extended use allows us to investigate their properties in depth. This experience is useful in the short term in refining our designs, and invaluable in the long term in advancing our knowledge. Most of the major advances in information systems have come through this strategy, including personal computing, distributed systems, and the Internet. We also perform complementary work of a more mathematical flavor. Some of it is in established fields of theoretical computer science, such as the analysis of algorithms, computational geometry, and logics of programming. Other work explores new ground motivated by problems that arise in our systems research. We have a strong commitment to communicating our results; exposing and testing our ideas in the research and development communities leads to improved understanding. Our research report series supplements publication in professional journals and conferences. We seek users for our prototype systems among those with whom we have common interests, and we encourage collaboration with university researchers.
A Guided Tour to Approximate String Matching
 ACM Computing Surveys
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining t ..."
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Cited by 418 (38 self)
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We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems. 1
OnLine Construction of Suffix Trees
, 1995
"... An online algorithm is presented for constructing the suffix tree for a given string in time linear in the length of the string. The new algorithm has the desirable property of processing the string symbol by symbol from left to right. It has always the suffix tree for the scanned part of the strin ..."
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Cited by 331 (2 self)
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An online algorithm is presented for constructing the suffix tree for a given string in time linear in the length of the string. The new algorithm has the desirable property of processing the string symbol by symbol from left to right. It has always the suffix tree for the scanned part of the string ready. The method is developed as a lineartime version of a very simple algorithm for (quadratic size) suffix tries. Regardless of its quadratic worstcase this latter algorithm can be a good practical method when the string is not too long. Another variation of this method is shown to give in a natural way the wellknown algorithms for constructing suffix automata (DAWGs).
Highorder entropycompressed text indexes
, 2003
"... We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet Σ, where each symbol is encoded by lg Σ  bits. We show that compressed suffix arrays use just nHh + O(n lg lg ..."
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Cited by 194 (22 self)
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We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet Σ, where each symbol is encoded by lg Σ  bits. We show that compressed suffix arrays use just nHh + O(n lg lg n / lg Σ  n) bits, while retaining full text indexing functionalities, such as searching any pattern sequence of length m in O(m lg Σ  + polylog(n)) time. The term Hh ≤ lg Σ  denotes the hthorder empirical entropy of the text, which means that our index is nearly optimal in space apart from lowerorder terms, achieving asymptotically the empirical entropy of the text (with a multiplicative constant 1). If the text is highly compressible so that Hh = o(1) and the alphabet size is small, we obtain a text index with o(m) search time that requires only o(n) bits. Further results and tradeoffs are reported in the paper. 1
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 182 (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 174 (79 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.
An O(ND) Difference Algorithm and Its Variations
 Algorithmica
, 1986
"... The problems of finding a longest common subsequence of two sequences A and B and a shortest edit script for transforming A into B have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a s ..."
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Cited by 159 (4 self)
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The problems of finding a longest common subsequence of two sequences A and B and a shortest edit script for transforming A into B have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a simple O(ND) time and space algorithm is developed where N is the sum of the lengths of A and B and D is the size of the minimum edit script for A and B. The algorithm performs well when differences are small (sequences are similar) and is consequently fast in typical applications. The algorithm is shown to have O(N +D expectedtime performance under a basic stochastic model. A refinement of the algorithm requires only O(N) space, and the use of suffix trees leads to an O(NlgN +D ) time variation.
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 152 (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.
Approaches to the Automatic Discovery of Patterns in Biosequences
, 1995
"... This paper is a survey of approaches and algorithms used for the automatic discovery of patterns in biosequences. Patterns with the expressive power in the class of regular languages are considered, and a classification of pattern languages in this class is developed, covering those patterns which a ..."
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Cited by 138 (21 self)
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This paper is a survey of approaches and algorithms used for the automatic discovery of patterns in biosequences. Patterns with the expressive power in the class of regular languages are considered, and a classification of pattern languages in this class is developed, covering those patterns which are the most frequently used in molecular bioinformatics. A formulation is given of the problem of the automatic discovery of such patterns from a set of sequences, and an analysis presented of the ways in which an assessment can be made of the significance and usefulness of the discovered patterns. It is shown that this problem is related to problems studied in the field of machine learning. The largest part of this paper comprises a review of a number of existing methods developed to solve this problem and how these relate to each other, focusing on the algorithms underlying the approaches. A comparison is given of the algorithms, and examples are given of patterns that have been discovered...