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Time-Space Trade-Offs for Longest Common Extensions
[article]
2013
arXiv
pre-print
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We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. ...
We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. ...
The longest common extension problem (LCE problem) is to preprocess T into a compact data structure supporting fast longest common extension queries. ...
arXiv:1211.0270v2
fatcat:7ovn7espzfg7nfeg3f2xtemulu
Time-Space Trade-Offs for Longest Common Extensions
[chapter]
2012
Lecture Notes in Computer Science
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We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T . ...
We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. ...
Acknowledgements We thank the anonymous referes for their valuable comments, and in particular for pointing out an issue with the preprocessing space of the randomised solution. ...
doi:10.1007/978-3-642-31265-6_24
fatcat:puexhxxzjnfjpmhda3qtbhsm6m
Time–space trade-offs for longest common extensions
2014
Journal of Discrete Algorithms
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We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T . ...
We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. ...
Acknowledgements We thank the anonymous referes for their valuable comments, and in particular for pointing out an issue with the preprocessing space of the randomised solution. ...
doi:10.1016/j.jda.2013.06.003
fatcat:tyahwybryvb7rlbgtclx6bgcwq
Tight Lower Bounds for the Longest Common Extension Problem
[article]
2017
arXiv
pre-print
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The longest common extension problem is to preprocess a given string of length n into a data structure that uses S(n) bits on top of the input and answers in T(n) time the queries LCE(i,j) computing the ...
It is known that this trade-off is tight. ...
The author wishes to acknowledge anonymous referees for detailed comments that helped to greatly improve the paper. ...
arXiv:1611.02891v5
fatcat:cut32cw3rjcrtdrtxjcu2zc5si
Longest Common Extensions in Sublinear Space
[chapter]
2015
Lecture Notes in Computer Science
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In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O( n τ ) space and O(τ ) query time. ...
The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. ...
The longest common extension problem (LCE problem) is to preprocess T into a compact data structure supporting fast longest common extension queries. ...
doi:10.1007/978-3-319-19929-0_6
fatcat:jedgbw4fdrcptlx4cwuflpaabu
Longest Common Extensions in Sublinear Space
[article]
2015
arXiv
pre-print
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In this paper we show that for any trade-off parameter 1 ≤τ≤ n, the problem can be solved in O(n/τ) space and O(τ) query time. ...
The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i,j) queries. ...
The longest common extension problem (LCE problem) is to preprocess T into a compact data structure supporting fast longest common extension queries. ...
arXiv:1504.02671v1
fatcat:virzw24iijaivpy5oyed3w3bma
Substring Complexity in Sublinear Space
[article]
2020
arXiv
pre-print
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We present the following results: an O(n^3/b^2)-time and O(b)-space algorithm to compute δ, for any b∈[1,n]; and an Õ(n^2/b)-time and O(b)-space algorithm to compute δ, for any b∈[n^2/3,n]. ...
In particular, δ≤γ always holds and δ can be computed in O(n) time using Ω(n) working space. ...
Given a string T of length n, we can compute δ = sup{S T (k)/k, k ≥ 1} inÕ(n 2 /b) time using O(b) space, for any b ∈ [n 2/3 , n]. ...
arXiv:2007.08357v1
fatcat:r54pfdn6tvfztcpg4h7lvgp4qm
Page 1171 of Mathematical Reviews Vol. , Issue 85c
[page]
1985
Mathematical Reviews
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Ja’Ja’, Joseph (1-PAS) 85c:68026 Time-space trade-offs for some algebraic problems. J. Assoc. Comput. Mach. 30 (1983), no. 3, 657-667. ...
For an application to pattern recognition, a discussion is presented on extensions to weighted longest common subsequences and to the longest common subma- trix.”
Vodop’yanov, V. K.; Zavyalov, V. ...
Sampled Longest Common Prefix Array
[chapter]
2010
Lecture Notes in Computer Science
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When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. ...
We show that when used with a compressed suffix array (CSA), the sampled LCP array often offers better time/space trade-offs than the existing alternatives. ...
While the suffix array and the LCP array can be compressed to a space relative to the number of of equal letter runs in BWT, no such representation is known for suffix tree topology. ...
doi:10.1007/978-3-642-13509-5_21
fatcat:ahsnbuzbyrgz3fydzi3iqewkrq
Longest common extensions in trees
2016
Theoretical Computer Science
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For LCETT queries, we present a time-space trade-off, that given any parameter τ , 1 ≤ τ ≤ n, leads to an O(nτ ) space and O(n/τ ) query-time solution (all of these bounds hold on a standard unit-cost ...
The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. ...
The Time-Space Trade-Off We now give a time-space trade-off for the LCE TT problem as stated by the following theorem. ...
doi:10.1016/j.tcs.2015.08.009
fatcat:agclladhdnbobatxasj27rkuwu
Longest Common Extensions in Trees
[article]
2015
arXiv
pre-print
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For queries, we present a time-space trade-off, that given any parameter τ, 1 ≤τ≤ n, leads to an O(nτ) space and O(n/τ) query-time solution. ...
The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. ...
The Time-Space Trade-Off We now give a time-space trade-off for the LCE TT problem as stated by the following theorem. ...
arXiv:1412.1254v3
fatcat:ehijuinpqjh7hca5ljhomihgjq
Longest Common Extensions in Trees
[chapter]
2015
Lecture Notes in Computer Science
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For LCETT queries, we present a time-space trade-off, that given any parameter τ , 1 ≤ τ ≤ n, leads to an O(nτ ) space and O(n/τ ) query-time solution. ...
The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. ...
We complement this result with a time-space trade-off that achieves O(nτ ) space and O(n/τ ) query time for any parameter 1 ≤ τ ≤ n. ...
doi:10.1007/978-3-319-19929-0_5
fatcat:7dhqd3ppajaufe4g3zaftoakvi
Sublinear Space Algorithms for the Longest Common Substring Problem
[chapter]
2014
Lecture Notes in Computer Science
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In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the LCS problem can be solved in O(τ ) space and O(n 2 /τ ) time, thus providing the first smooth deterministic timespace trade-off from ...
This problem is known as the longest common substring (LCS) problem and has a classic O(n) space and O(n) time solution (Weiner [FOCS'73], Hui [CPM'92]). ...
Below we show a time-space trade-off lower bound for element bidistinctness. Lemma 9. If |D| ≥ 2n 2 , at least a fraction 1/e of inputs belong to EB −1 (1). Proof. ...
doi:10.1007/978-3-662-44777-2_50
fatcat:lsgrntujabfenn7zv36krheuma
Sublinear Space Algorithms for the Longest Common Substring Problem
[article]
2014
arXiv
pre-print
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In this paper we show that for any trade-off parameter 1 ≤τ≤ n, the LCS problem can be solved in O(τ) space and O(n^2/τ) time, thus providing the first smooth deterministic time-space trade-off from constant ...
This problem is known as the longest common substring (LCS) problem and has a classic O(n) space and O(n) time solution (Weiner [FOCS'73], Hui [CPM'92]). ...
Below we show a time-space trade-off lower bound for element bidistinctness. Lemma 9. If |D| ≥ 2n 2 , at least a fraction 1/e of inputs belong to EB −1 (1). Proof. ...
arXiv:1407.0522v1
fatcat:reuwyixidjb5dchgvrsfgrzvzy
Fast Longest Common Extensions in Small Space
[article]
2016
arXiv
pre-print
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In this paper we address the longest common extension (LCE) problem: to compute the length ℓ of the longest common prefix between any two suffixes of T∈Σ^n with Σ = {0, ...σ-1} . ...
Our results improve the state of the art in space usage, query times, and preprocessing times and are extremely practical: we present a C++ implementation that is very fast and space-efficient in practice ...
The longest common extension (LCE) problem asks to build a data structure on T supporting fast LCE queries: given 0 ≤ i, j < n, return the length ℓ = LCE(i, j) of the longest common prefix of T [i, . . ...
arXiv:1607.06660v1
fatcat:2bcauasygrhkrdsy253fzznjmm
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