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Computing Covers under Substring Consistent Equivalence Relations [article]

Natsumi Kikuchi, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
2020 arXiv   pre-print
An equivalence relation ≈ over strings is called a substring consistent equivalence relation (SCER) iff X ≈ Y implies (1) |X| = |Y| and (2) X[i:j] ≈ Y[i:j] for all 1 < i < j < |X|.  ...  In this paper, we generalize the notion of covers for SCERs and prove that existing algorithms to compute the shortest cover array and the longest cover array of a string T under the identity relation  ...  Definition 1 (Substring Consistent Equivalence Relation (SCER) ≈).  ... 
arXiv:2002.06764v2 fatcat:wefznf6odjg3phfserxk7cek2i

Generalized approximate regularities in strings

Hui Zhang, Qing Guo, Costas S. Iliopoulos
2008 International Journal of Computer Mathematics  
Given a string x of length n and an integer λ, the minimum approximate λ-cover (resp. seed) problem is to find a set of λ substrings each of equal length that covers x (resp. a superstring of x) with the  ...  minimum error, under a variety of distance models containing the Hamming distance, the edit distance and the weighted edit distance.  ...  Note that ECT is built along with the partitioning of equivalence classes. When all the equivalence classes for p-substrings are computed, the corresponding nodes of depth p are added into ECT.  ... 
doi:10.1080/00207160701389168 fatcat:qnrb7ega45fdjidtz6yqwwlopa

Genomic Distances under Deletions and Insertions

Mark Marron, Krister M. Swenson, Bernard M.E. Moret
2004 Theoretical Computer Science  
We derive an error bound for our polynomial-time distance computation under various assumptions and present preliminary experimental results that suggest that performance in practice may be excellent,  ...  In this paper we extend El-Mabrouk's work to handle duplications as well as insertions and present an alternate framework for computing (near) minimal edit sequences involving insertions, deletions, and  ...  This work is supported by the National Science Foundation under grants ACI 00-81404, DEB 01-20709, EIA 01-13095, EIA 01-21377, and EIA 02-03584.  ... 
doi:10.1016/j.tcs.2004.02.039 fatcat:6hjzacvhpbbmdbxzfyxmy2y3tu

Genomic Distances under Deletions and Insertions [chapter]

Mark Marron, Krister M. Swenson, Bernard M. E. Moret
2003 Lecture Notes in Computer Science  
We derive an error bound for our polynomial-time distance computation under various assumptions and present preliminary experimental results that suggest that performance in practice may be excellent,  ...  In this paper we extend El-Mabrouk's work to handle duplications as well as insertions and present an alternate framework for computing (near) minimal edit sequences involving insertions, deletions, and  ...  This work is supported by the National Science Foundation under grants ACI 00-81404, DEB 01-20709, EIA 01-13095, EIA 01-21377, and EIA 02-03584.  ... 
doi:10.1007/3-540-45071-8_54 fatcat:tfee3g6jd5fjhdtifksjaqecma

Discovering characteristic expressions in literary works

Masayuki Takeda, Tetsuya Matsumoto, Tomoko Fukuda, Ichiro Nanri
2003 Theoretical Computer Science  
In this paper, we propose partitioning the text substrings into equivalence classes under an equivalence relation on strings, originally deÿned by Blumer et al. (J. ACM 34 (3) (1987) 578 ).  ...  The equivalence relation has the desirable property that all members of each equivalence class necessarily have a unique goodness value.  ...  One is to partition text substrings into equivalence classes under an equivalence relation on strings, and to create a list of these and let the experts examine the equivalence classes one by one.  ... 
doi:10.1016/s0304-3975(02)00185-8 fatcat:md2lvuj4yjepzix7hy3f54xr5u

Maximal and minimal representations of gapped and non-gapped motifs of a string

Esko Ukkonen
2009 Theoretical Computer Science  
We apply two equivalence relations on representations. The first one is the well-known occurrence-equivalence of motifs.  ...  For both equivalences, quadratic-time algorithms are given for finding a maximal representative of an equivalence class. Finding a minimal representative is shown to be NP-complete in both cases.  ...  The author was supported by the Academy of Finland under grants 21196 (From Data to Knowledge) and 7523004 (Algorithmic Data Analysis).  ... 
doi:10.1016/j.tcs.2009.07.015 fatcat:htkgfzgtkfd6lppam56wsofvze

String Pattern Matching for a Deluge Survival Kit [chapter]

Alberto Apostolico, Maxime Crochemore
2002 Massive Computing  
Recall that the index of an equivalence relation is the number of equivalence classes in it. Lemma 12 The index k of~he equivalence relation =:1: obeys k < 2n.  ...  Our automaton recognizes the (finite) language consisting of all substrings of string x.  ... 
doi:10.1007/978-1-4615-0005-6_6 fatcat:zx3uoflljbfs7oyclwxk2ic2ua

The string-to-string correction problem with block moves

Walter F. Tichy
1984 ACM Transactions on Computer Systems  
The algorithm is optimal in the sense that it generates a minimal, covering set of common subsLrings of one string with respecllo the oLher.  ...  Extant algorithms compute a Longest Common Subsequence (LeS) of the twa strings and then regard the characters not included in the LCS as the differences.  ...  A related application can be found in screen editors and This work WIlS 9~pport(:d in pUTt by the Nationnl Science~ound8l.ion under grant MeS· 6109513. graphics packages.  ... 
doi:10.1145/357401.357404 fatcat:kjguhxpvgbdnle3bs3vnrly2v4

Joint repairs for web wrappers

Stefano Ortona, Giorgio Orsi, Tim Furche, Marcello Buoncristiano
2016 2016 IEEE 32nd International Conference on Data Engineering (ICDE)  
We study the problem of computing joint repairs for XPath-based wrappers and their extracted data.  ...  We show that the problem is NP-complete in general but becomes tractable under a few natural assumptions.  ...  The computation stops here as the set {s 1 , s 2 } covers the entire relation.  ... 
doi:10.1109/icde.2016.7498320 dblp:conf/icde/OrtonaOFB16 fatcat:afuyusvp4jgwnirgoily55u5yq

Computing NP-hard Repetitiveness Measures via MAX-SAT [article]

Hideo Bannai and Keisuke Goto and Masakazu Ishihata and Shunsuke Kanda and Dominik Köppl and Takaaki Nishimoto
2022 arXiv   pre-print
Alas, the computation of some of these measures is NP-hard, and straight-forward computation is infeasible for datasets of even small sizes.  ...  While a vast variety of implementations for heuristically computing approximations exist, exact computation of these measures has received little to no attention.  ...  [5] based on an equivalence relation over substrings of T , and their number is known to be O(n) (Lemma 3 in [30]). Hence, the total size of the CNF is reduced to O(mn) ⊆ O(n 2 ).  ... 
arXiv:2207.02571v2 fatcat:gqmbuldgnjawdktmtmtwljdkq4

Range Shortest Unique Substring Queries [chapter]

Paniz Abedin, Arnab Ganguly, Solon P. Pissis, Sharma V. Thankachan
2019 Lecture Notes in Computer Science  
Repeats and unique substrings are of great interest in computational biology and in information retrieval.  ...  A substring T[i, j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T.  ...  Given a position i of T, return a shortest unique substring of T covering i.  ... 
doi:10.1007/978-3-030-32686-9_18 fatcat:4th7hkls2ngntj5z2podo4fvje

Rich Queries on Encrypted Data: Beyond Exact Matches [chapter]

Sky Faber, Stanislaw Jarecki, Hugo Krawczyk, Quan Nguyen, Marcel Rosu, Michael Steiner
2015 Lecture Notes in Computer Science  
Related Work. The only work we are aware of that addresses substring search on symmetrically encrypted data is the work of Chase and Shen [9] .  ...  Range queries are supported in the multi-writer public key setting by Boneh-Waters [4] and Shi et al. [24] but at a significantly higher computational cost.  ...  query consists of a single substring.  ... 
doi:10.1007/978-3-319-24177-7_7 fatcat:fcjyyeqaifg7xnfa4azfom3sly

Complexity of Approximating Closest Substring Problems [chapter]

Patricia A. Evans, Andrew D. Smith
2003 Lecture Notes in Computer Science  
Related problems differing only in their objective functions, seeking either to maximize the number of strings covered by the substring or maximize the length of the substring, are also examined and bounds  ...  The closest substring problem, where a short string is sought that minimizes the number of mismatches between it and each of a given set of strings, is a minimization problem with a polynomial time approximation  ...  We call any partition of F whose equivalence relation is the property of having an exact common substring a substring induced partition.  ... 
doi:10.1007/978-3-540-45077-1_20 fatcat:zztwrvffgvhuflwxeb33qaipwq

FootPrinter3: phylogenetic footprinting in partially alignable sequences

F. Fang, M. Blanchette
2006 Nucleic Acids Research  
to exploit the wealth of vertebrate genomes being sequenced, as it allows taking full advantage of the sequences of highly diverged species (e.g. chicken, zebrafish), as well as those of more closely related  ...  A motif is consistent with a set of alignment blocks if the substrings it contains could form a new alignment block that would not violate the partial order relation defined by the existing blocks [see  ...  In Figure 1 , the red motif consists of a substring of each of the input sequences (with two candidates from zebrafish).  ... 
doi:10.1093/nar/gkl123 pmid:16845084 pmcid:PMC1538810 fatcat:w27r7ktsdbebtmj3pnnd2f5soy

On-line Minimum Closed Covers [chapter]

Costas S. Iliopoulos, Manal Mohamed
2014 IFIP Advances in Information and Communication Technology  
The Minimum Closed Covers problem asks us to compute a minimum size of a closed cover of given string.  ...  We also show a method to recover a minimum closed cover of each prefix of w in greedy manner from right to left.  ...  Also, the λ-covers problem finds a minimum set of λ substrings of equal length that covers w with the minimum error, under a variety of distance models [12] .  ... 
doi:10.1007/978-3-662-44722-2_12 fatcat:a7gmrmlvabhnbbal4mtltj3ay4
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