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166
The String BTree: A New Data Structure for String Search in External Memory and its Applications.
 Journal of the ACM
, 1998
"... We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by a ..."
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Cited by 138 (12 self)
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We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String BTree overcomes the theoretical limitations of inverted files, Btrees, prefix Btrees, suffix arrays, compacted tries and suffix trees. String Btrees have the same worstcase performance as Btrees but they manage unboundedlength strings and perform much more powerful search operations such as the ones supported by suffix trees. String Btrees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication.
Hot sax: Efficiently finding the most unusual time series subsequence
, 2005
"... In this work, we introduce the new problem of finding time series discords. Time series discords are subsequences of a longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. Ti ..."
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Cited by 103 (4 self)
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In this work, we introduce the new problem of finding time series discords. Time series discords are subsequences of a longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. Time series discords have many uses for data mining, including improving the quality of clustering, data cleaning, summarization, and anomaly detection. As we will show, discords are particularly attractive as anomaly detectors because they only require one intuitive parameter (the length of the subsequence) unlike most anomaly detection algorithms that typically require many parameters. We evaluate our work with a comprehensive set of experiments. In particular, we demonstrate the utility of discords with objective experiments on domains as diverse as Space Shuttle telemetry monitoring, medicine, surveillance, and industry, and we demonstrate the effectiveness of our discord discovery algorithm with more than one million experiments, on 82 different datasets from diverse domains.
An Experimental Study of an Opportunistic Index
 In SODA
, 2001
"... The size of electronic data is currently growing at a faster rate than computer memory and disk storage capacities. For this reason compression appears always as an attractive choice, if not mandatory. However space overhead is not the only resource to be optimized when managing large data collectio ..."
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Cited by 79 (6 self)
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The size of electronic data is currently growing at a faster rate than computer memory and disk storage capacities. For this reason compression appears always as an attractive choice, if not mandatory. However space overhead is not the only resource to be optimized when managing large data collections; in fact data turn out to be useful only when properly indexed to support search operations that efficiently extract the userrequested information. Approaches to combine compression and indexing techniques are nowadays receiving more and more attention. A rst step towards the design of a compressed fulltext index achieving guaranteed performance in the worst case has been recently done in [10]. This index combines the compression algorithm proposed by Burrows and Wheeler [5] with the sux array data structure [16]. The index is opportunistic in that it takes advantage of the compressibility of the input data by decreasing the space occupancy at no signi cant asymptotic slowdown in the query performance. In this paper we present an implementation of this index and perform an extensive set of experiments on various text collections. The experiments show that our index is compact (its space occupancy is close to the one achieved by the best known compressors), it is fast in counting the number of pattern occurrences, and the cost of their retrieval is reasonable when they are few (i.e., in case of a selective query). In addition, our experiments show that the FMindex is exible in that it is possible to trade space occupancy for search time by choosing the amount of auxiliary information stored into it. 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 79 (3 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 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 76 (12 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.
FASTER SUFFIX SORTING
, 1999
"... We propose a fast and memory efficient algorithm for lexicographically sorting the suffixes of a string, a problem that has important applications in data compression as well as string matching. Our ..."
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Cited by 60 (2 self)
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We propose a fast and memory efficient algorithm for lexicographically sorting the suffixes of a string, a problem that has important applications in data compression as well as string matching. Our
Dynamical Sources in Information Theory: A General Analysis of Trie Structures
 ALGORITHMICA
, 1999
"... Digital trees, also known as tries, are a general purpose flexible data structure that implements dictionaries built on sets of words. An analysis is given of three major representations of tries in the form of arraytries, list tries, and bsttries ("ternary search tries"). The size an ..."
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Cited by 60 (7 self)
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Digital trees, also known as tries, are a general purpose flexible data structure that implements dictionaries built on sets of words. An analysis is given of three major representations of tries in the form of arraytries, list tries, and bsttries ("ternary search tries"). The size and the search costs of the corresponding representations are analysed precisely in the average case, while a complete distributional analysis of height of tries is given. The unifying data model used is that of dynamical sources and it encompasses classical models like those of memoryless sources with independent symbols, of finite Markovchains, and of nonuniform densities. The probabilistic behaviour of the main parameters, namely size, path length, or height, appears to be determined by two intrinsic characteristics of the source: the entropy and the probability of letter coincidence. These characteristics are themselves related in a natural way to spectral properties of specific transfer operators of the Ruelle type.
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 59 (6 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
Lower bounds for high dimensional nearest neighbor search and related problems
, 1999
"... In spite of extensive and continuing research, for various geometric search problems (such as nearest neighbor search), the best algorithms known have performance that degrades exponentially in the dimension. This phenomenon is sometimes called the curse of dimensionality. Recent results [38, 37, 40 ..."
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Cited by 55 (2 self)
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In spite of extensive and continuing research, for various geometric search problems (such as nearest neighbor search), the best algorithms known have performance that degrades exponentially in the dimension. This phenomenon is sometimes called the curse of dimensionality. Recent results [38, 37, 40] show that in some sense it is possible to avoid the curse of dimensionality for the approximate nearest neighbor search problem. But must the exact nearest neighbor search problem suffer this curse? We provide some evidence in support of the curse. Specifically we investigate the exact nearest neighbor search problem and the related problem of exact partial match within the asymmetric communication model first used by Miltersen [43] to study data structure problems. We derive nontrivial asymptotic lower bounds for the exact problem that stand in contrast to known algorithms for approximate nearest neighbor search. 1
Burst Tries: A Fast, Efficient Data Structure for String Keys
 ACM Transactions on Information Systems
, 2002
"... Many applications depend on efficient management of large sets of distinct strings in memory. For example, during index construction for text databases a record is held for each distinct word in the text, containing the word itself and information such as counters. We propose a new data structure, t ..."
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Cited by 42 (10 self)
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Many applications depend on efficient management of large sets of distinct strings in memory. For example, during index construction for text databases a record is held for each distinct word in the text, containing the word itself and information such as counters. We propose a new data structure, the burst trie, that has significant advantages over existing options for such applications: it requires no more memory than a binary tree; it is as fast as a trie; and, while not as fast as a hash table, a burst trie maintains the strings in sorted or nearsorted order. In this paper we describe burst tries and explore the parameters that govern their performance. We experimentally determine good choices of parameters, and compare burst tries to other structures used for the same task, with a variety of data sets. These experiments show that the burst trie is particularly effective for the skewed frequency distributions common in text collections, and dramatically outperforms all other data structures for the task of managing strings while maintaining sort order.