Re-pair Achieves High-Order Entropy

Navarro, Gonzalo; S.​Russo, Luís M.

doi:10.1109/dcc.2008.79

Cited by 21 publications

(19 citation statements)

References 15 publications

(23 reference statements)

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“…mr |, 1 2 g rp < g mr ≤ g rp follows Equations (11) and (12), and thus, the proposition holds. g mr = g rp holds when every length l…”

Section: Definition 3 (Mr-repair)mentioning

confidence: 67%

“…Despite its simple scheme, RePair is known for its high compression in practice [3][4][5], and hence, it has been comprehensively studied. Some examples of studies on the RePair algorithm include its extension to an online algorithm [6], practical working time/space improvements [7,8], applications to various fields [3,9,10], and theoretical analysis of generated grammar sizes [1,11,12].…”

Section: Introductionmentioning

confidence: 99%

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Practical Grammar Compression Based on Maximal Repeats

et al. 2020

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This study presents an analysis of RePair, which is a grammar compression algorithm known for its simple scheme, while also being practically effective. First, we show that the main process of RePair, that is, the step by step substitution of the most frequent symbol pairs, works within the corresponding most frequent maximal repeats. Then, we reveal the relation between maximal repeats and grammars constructed by RePair. On the basis of this analysis, we further propose a novel variant of RePair, called MR-RePair, which considers the one-time substitution of the most frequent maximal repeats instead of the consecutive substitution of the most frequent pairs. The results of the experiments comparing the size of constructed grammars and execution time of RePair and MR-RePair on several text corpora demonstrate that MR-RePair constructs more compact grammars than RePair does, especially for highly repetitive texts.

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“…mr |, 1 2 g rp < g mr ≤ g rp follows Equations (11) and (12), and thus, the proposition holds. g mr = g rp holds when every length l…”

Section: Definition 3 (Mr-repair)mentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Practical Grammar Compression Based on Maximal Repeats

et al. 2020

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“…(It is sometimes desirable for the CFG to be in Chomsky normal form (CNF), in which case it is also known as a straight-line program.) We can measure our success in terms of universality [5], empirical entropy [6] or the ratio between the size of our CFG and the size g = Ω(log n) of the smallest such grammar. In this paper we consider the third and last measure.…”

Section: Introductionmentioning

confidence: 99%

Grammar-Based Compression in a Streaming Model

Gagie

Gawrychowski

2010

Language and Automata Theory and Applications

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We show that, given a string s of length n, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates s and only s and whose size is within an O min g log g, n/ log n -factor of the minimum g.This stands in contrast to our previous result that, with polylogarithmic memory and polylogarithmic passes over a single stream, we cannot build such a grammar whose size is within any polynomial of g.

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“…The Re-Pair algorithm is an algorithm with O(n) time complexity; it is easy to implement using linked lists and a priority queue. Further, it was shown in [18] that it can compress an input message of length n over an alphabet of size |Σ| into at most 2H k + o(n log |Σ|) bits, where H k is k-th order entropy.…”

Section: Previous Workmentioning

confidence: 99%

Prediction and Evaluation of Zero Order Entropy Changes in Grammar-Based Codes

Vašínek

Platoš

2017

Entropy

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Abstract:The change of zero order entropy is studied over different strategies of grammar production rule selection. The two major rules are distinguished: transformations leaving the message size intact and substitution functions changing the message size. Relations for zero order entropy changes were derived for both cases and conditions under which the entropy decreases were described. In this article, several different greedy strategies reducing zero order entropy, as well as message sizes are summarized, and the new strategy MinEnt is proposed. The resulting evolution of the zero order entropy is compared with a strategy of selecting the most frequent digram used in the Re-Pair algorithm.

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Re-pair Achieves High-Order Entropy

Cited by 21 publications

References 15 publications

Practical Grammar Compression Based on Maximal Repeats

Practical Grammar Compression Based on Maximal Repeats

Grammar-Based Compression in a Streaming Model

Prediction and Evaluation of Zero Order Entropy Changes in Grammar-Based Codes

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