Computing Longest Previous Factor in linear time and applications

Crochemore, Maxime; Ilie, Lucian

doi:10.1016/j.ipl.2007.10.006

Cited by 113 publications

(140 citation statements)

References 16 publications

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“…It has been noticed in [4] that the content of the LPF table is the same as that of the LCP table up to some permutation. A question arises then: what permutation is it?…”

Section: Sorting Networkmentioning

confidence: 99%

“…For example, the algorithm in [14] reports all maximal repetitions (called runs) occurring in a string in O(|y| log |A|) time. It runs in linear time if a Suffix Array is used instead of a Suffix Tree [4]. Indeed the technique seems to be the only technique that leads to linear-time algorithms independently of the alphabet size for this type of question.…”

Section: Longest Previous Factormentioning

confidence: 99%

“…A graphical representation of the Suffix Array structure helps understand the design of the algorithms. The Longest Previous Factor is coined in [4], where a linear-time computation is described and applied to LZ77 factorisation. Another version running on-line on the Suffix Array of the text and requiring only O( √ n) extra memory space is shown in [5].…”

Section: Longest Previous Factormentioning

confidence: 99%

“…First, an algorithm similar to the one in [4] is described. The algorithm is regarded in Section 3 as using the Suffix Array like a sorting network.…”

Section: Longest Previous Factormentioning

confidence: 99%

“…LPF-simple(SUF, LCP, n) The array next can alternatively be pre-computed by the following procedure whose linear-time behaviour is an interesting exercise left to the reader. The procedure also computes the array LPF > defined in [4] and that accounts for larger ranks only. It is defined, for r = 0, .…”

Section: Using a Suffix Arraymentioning

confidence: 99%

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LPF Computation Revisited

Crochemore

Ilie

Iliopoulos

et al. 2009

Lecture Notes in Computer Science

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Abstract. We present efficient algorithms for storing past segments of a text. They are computed using two previously computed read-only arrays (SUF and LCP) composing the Suffix Array of the text. They compute the maximal length of the previous factor (subword) occurring at each position of the text in a table called LPF. This notion is central both in many conservative text compression techniques and in the most efficient algorithms for detecting motifs and repetitions occurring in a text. The main results are: a linear-time algorithm that computes explicitly the permutation that transforms the LCP table into the LPF table; a time-space optimal computation of the LPF table; and an O(n log n) strong in-place computation of the LPF table.

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“…It has been noticed in [4] that the content of the LPF table is the same as that of the LCP table up to some permutation. A question arises then: what permutation is it?…”

Section: Sorting Networkmentioning

confidence: 99%

Section: Longest Previous Factormentioning

confidence: 99%

Section: Longest Previous Factormentioning

confidence: 99%

“…First, an algorithm similar to the one in [4] is described. The algorithm is regarded in Section 3 as using the Suffix Array like a sorting network.…”

Section: Longest Previous Factormentioning

confidence: 99%

Section: Using a Suffix Arraymentioning

confidence: 99%

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LPF Computation Revisited

Crochemore

Ilie

Iliopoulos

et al. 2009

Lecture Notes in Computer Science

Self Cite

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Improving a lightweight LZ77 computation algorithm for running faster

Liu

Nong

Chan

et al. 2015

Softw. Pract. Exper.

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SUMMARYComputing the Lempel-Ziv factorization (LZ77) of a string is a key step in many applications. However, at the same time, it constitutes a bottleneck of the entire computation. The investigation of time and space efficient computation of the LZ77 has become an important topic. In this paper, we present a lightweight linear-time algorithm called LZone for computing the LZ77, which is designed by improvements on the existing linear-time space efficient LZ77 algorithm BGone for speed acceleration. For an input string T OE1::n over a constant alphabet size of O.1/, LZone requires only n words of workspace in addition to the input string and the output factorization, dlog ne bits per word. This is the same space requirement for the algorithm BGone. LZone has two versions, LZoneT and LZoneSA, corresponding to BGoneT and BGoneSA, respectively. Our experimental results show that for computing the LZ77 from an input string T , LZoneT and LZoneSA run at around 26% and 57%, respectively, faster than their counterparts in BGone. Moreover, for computing the LZ77 from the suffix array of T , the speed of LZoneSA is on average twice that of BGoneSA.

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An Approach for LPF Table Computation

Chairungsee

Charuphanthuset

2019

Communications in Computer and Information Science

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Computing Longest Previous Factor in linear time and applications

Cited by 113 publications

References 16 publications

LPF Computation Revisited

LPF Computation Revisited

Improving a lightweight LZ77 computation algorithm for running faster

An Approach for LPF Table Computation

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