Efficient algorithms to compute compressed longest common substrings and compressed palindromes

Matsubara, Wataru; Inenaga, Shunsuke; Ishino, Akira; Shinohara, Ayumi; Nakamura, Tomoyuki; Hashimoto, Kazuo

doi:10.1016/j.tcs.2008.12.016

Cited by 57 publications

(31 citation statements)

References 4 publications

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“…If we allow no gaps in palindromes (i.e., if we set g = 0), then Result 2 implies that we can compute a compact representation of all maximal palindromes in O (n 3 h) time and O (n 2 ) space. Hence, Result 2 can be seen as a generalization of the work by Matsubara et al [16] with the same efficiency.…”

Section: Introductionsupporting

confidence: 64%

“…Independently, Khvorost [9] presented an algorithm for computing a compact representation of all squares in s in O (n 3 h log 2 N) time and O (n 2 ) space. Matsubara et al [16] showed that a compact representation of all maximal palindromes occurring in the string s can be computed in O (n 3 h) time and O (n 2 ) space. Note that the length N of the decompressed string s can be as large as O (2 n ) in the worst case.…”

Section: Introductionmentioning

confidence: 99%

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Detecting regularities on grammar-compressed strings

Tomohiro

Matsubara

Shimohira

et al. 2015

Information and Computation

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We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s inh is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O (n 3 h + gnh log N) time and O (n 2 ) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O (n 2 h) time and O (nh(n + log 2 N)) time, respectively.

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Section: Introductionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Detecting regularities on grammar-compressed strings

Tomohiro

Matsubara

Shimohira

et al. 2015

Information and Computation

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“…The reversed SLP S ′ contains n production rules and the transformation ensures that t X i ′ = t R X i for each production rule X i ′ in S ′ . A proof of this can be found in [12]. Producing the reversed SLP takes linear time and in the process we create pointers from each variable to its corresponding variable in the reversed SLP.…”

Section: Prefix and Suffix Decompressionmentioning

confidence: 99%

Compact q-gram profiling of compressed strings

Bille¹,

Cording²,

Gørtz³

2014

Theoretical Computer Science

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We consider the problem of computing the q-gram profile of a string T of size N compressed by a context-free grammar with n production rules. We present an algorithm that runs in O(N − α) expected time and uses O(n + q + k T,q ) space, where N − α ≤ qn is the exact number of characters decompressed by the algorithm and k T,q ≤ N − α is the number of distinct q-grams in T . This simultaneously matches the current best known time bound and improves the best known space bound. Our space bound is asymptotically optimal in the sense that any algorithm storing the grammar and the q-gram profile must use Ω(n + q + k T,q ) space. To achieve this we introduce the q-gram graph that space-efficiently captures the structure of a string with respect to its q-grams, and show how to construct it from a grammar.

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“…We will use the following results: We can easily extend the above theorem for computing longest common suffixes, by e.g., pre-computing the SLPs of the reversed strings of T and P . Those SLPs have a total of m + n size and can be computed in O(n + m) time (see [10], Lemma 1).…”

Section: Algorithmmentioning

confidence: 99%