Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications

Kasai, Takeshi; Lee, Gun-Ho; Arimura, Hiroki; Arikawa, Setsuo; Park, Kunsoo

doi:10.1007/3-540-48194-x_17

Cited by 363 publications

(265 citation statements)

References 18 publications

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“…Task (2) is related to our choice of implementing compressed suffix arrays using structures evolved from FM-index [Ferragina and Manzini 2005], and is tackled in this paper. Also for task (3) our solution variates slightly from [Hon and Sadakane 2002] as we build on top of the suffixes-insertion algorithm [Crochemore and Rytter 2002] and they build on top of the post-order traversal algorithm of [Kasai et al 2001]. The final timerequirement of our implementation is O(n log n log |Σ|), being reasonably close to the best current theoretical result [Hon et al 2003a].…”

Section: Introductionmentioning

confidence: 72%

“…[ Kasai et al 2001] gave a linear time algorithm to construct the lcp-array given SA. One could use it to construct the encoding H by applying what is described above, but the intermediate lcp-array would take n log n bits.…”

Section: Space-efficient Construction Via Kasai Et Al Algorithmmentioning

confidence: 99%

“…One could use it to construct the encoding H by applying what is described above, but the intermediate lcp-array would take n log n bits. Instead, one can easily modify Kasai et al algorithm [Kasai et al 2001]. This has the consequence that one can can compute the lcp-values in the text order, at each step taking advantage of the already computed prefix length in the previous step:…”

Section: Space-efficient Construction Via Kasai Et Al Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Engineering a Compressed Suffix Tree Implementation

Välimäki

Gerlach

Dixit

et al. 2007

Experimental Algorithms

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Suffix tree is one of the most important data structures in string algorithms and biological sequence analysis. Unfortunately, when it comes to implementing those algorithms and applying them to real genomic sequences, often the main memory size becomes the bottleneck. This is easily explained by the fact that while a DNA sequence of length n from alphabet Σ = {A, C, G, T } can be stored in n log |Σ| = 2n bits, its suffix tree occupies O(n log n) bits. In practice, the size difference easily reaches factor 50.We report on an implementation of the compressed suffix tree very recently proposed by Sadakane (Theory of Computing Systems, in press). The compressed suffix tree occupies space proportional to the text size, i.e. O(n log |Σ|) bits, and supports all typical suffix tree operations with at most log n factor slowdown. Our experiments show that, e.g. on a 10 MB DNA sequence, the compressed suffix tree takes 10% of the space of the normal suffix tree. At the same time, a representative algorithm is slowed down by factor 30.Our implementation follows the original proposal in spirit, but some internal parts are tailored towards practical implementation. Our construction algorithm has time requirement O(n log n log |Σ|) and uses closely the same space as the final structure while constructing it: on the 10 MB DNA sequence, the maximum space usage during construction is only 1.5 times the final product size. As by-products, we develop a method to create Succinct Suffix Array directly from Burrows-Wheeler transform and a space-efficient version of suffixes-insertion algorithm to build balanced parentheses representation of suffix tree from LCP information.

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Section: Introductionmentioning

confidence: 72%

Section: Space-efficient Construction Via Kasai Et Al Algorithmmentioning

confidence: 99%

Section: Space-efficient Construction Via Kasai Et Al Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Engineering a Compressed Suffix Tree Implementation

Välimäki

Gerlach

Dixit

et al. 2007

Experimental Algorithms

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“…Without loss of generality, assume that w 2 must follow w 1 . It means that w 2 can appear only after w 1 appears at least R 1 times.…”

Section: Problemmentioning

confidence: 99%

An Algorithm for the Generalized k-Keyword Proximity Problem and Finding Longest Repetitive Substring in a Set of Strings

Lee

Kim

2006

Computational Science – ICCS 2006

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Abstract. The data grid may consist of huge number of documents and the number of documents which contain the keywords in the query may be very large. Therefore, we need some method to measure the relevance of the documents to the query. In this paper we propose algorithms for computing k-keyword proximity score [3] in more realistic environments. Furthermore, we show that they can be used to find longest repetitive substring with constraints in a set of strings.

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“…We note that the suffix tree algorithm is simulated by a suffix array structure, using the method presented in [17,18].…”

Section: Computational Experimentsmentioning

confidence: 99%

Practical Algorithms for Pattern Based Linear Regression

et al. 2005

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Abstract. We consider the problem of discovering the optimal pattern from a set of strings and associated numeric attribute values. The goodness of a pattern is measured by the correlation between the number of occurrences of the pattern in each string, and the numeric attribute value assigned to the string. We present two algorithms based on suffix trees, that can find the optimal substring pattern in O(N n) and O(N 2 ) time, respectively, where n is the number of strings and N is their total length. We further present a general branch and bound strategy that can be used when considering more complex pattern classes. We also show that combining the O(N 2 ) algorithm and the branch and bound heuristic increases the efficiency of the algorithm considerably.

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Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications

Cited by 363 publications

References 18 publications

Engineering a Compressed Suffix Tree Implementation

Engineering a Compressed Suffix Tree Implementation

An Algorithm for the Generalized k-Keyword Proximity Problem and Finding Longest Repetitive Substring in a Set of Strings

Practical Algorithms for Pattern Based Linear Regression

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