Efficient string-matching allowing for non-overlapping inversions

Cantone, Domenico; Cristofaro, Salvatore; Faro, Simone

doi:10.1016/j.tcs.2012.06.009

Cited by 24 publications

(8 citation statements)

References 8 publications

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“…Regarding the alignment problem with translocations, Cho et al [13] presented a first solution for the case of inversions and translocations of equal length factors (i.e., balanced translocations), working in O(n 3 )-time and O(m 2 )-space. However their solution generalizes the problem to the case where edit operations Authors Year W.C. Time AVG Time Space Alignment with inversions Schoniger and Waterman [26] (1992) O(n 2 m 2 ) -O(m 2 ) Gao et al [19] (2003) O(n 2 m 2 ) -O(nm) Chen et al [12] (2004) O(n 2 m 2 ) -O(nm) Alves et al [5] (2005) O(n 3 log n) -O(n 2 ) Vellozo et al [27] (2006) O(nm 2 ) -O(nm) Alignment with inversions and balanced translocations on both strings Cho et al [13] (2015) O(m 3 ) -O(m 2 ) Pattern matching with inversions Cantone et al [6] (2011) O(nm) -O(m 2 ) Cantone et al [7] (2013) O(nm) O(n) O(m 2 ) Pattern matching with unbalanced translocations Faro and Pavone [18] (2019) O(m 2 ) O(n) O(m) Pattern matching with inversions and balanced translocations Cantone et al [8] (2010) O(nm 2 ) O(n log m) O(m 2 ) Grabowski et al [20] (2011) O(nm 2 ) O(n) O(m) Cantone et al [9] ( Table 1. Results related to alignment and matching of strings allowing for inversions and translocations of factors.…”

Section: Related Resultsmentioning

confidence: 99%

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Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Cantone,

Faro,

Pavone

2021

Preprint

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In this paper we investigate the approximate string matching problem when the allowed edit operations are non-overlapping unbalanced translocations of adjacent factors. Such kind of edit operations take place when two adjacent sub-strings of the text swap, resulting in a modified string. The two involved substrings are allowed to be of different lengths. Such large-scale modifications on strings have various applications. They are among the most frequent chromosomal alterations, accounted for 30% of all losses of heterozygosity, a major genetic event causing inactivation of cancer suppressor genes. In addition, among other applications, they are frequent modifications accounted in musical or in natural language information retrieval. However, despite of their central role in so many fields of text processing, little attention has been devoted to the problem of matching strings allowing for this kind of edit operation. In this paper we present three algorithms for solving the problem, all of them with a O(nm 3 ) worst-case and a O(m 2 )-space complexity, where m and n are the length of the pattern and of the text, respectively. In particular, our first algorithm is based on the dynamic-programming approach. Our second solution improves the previous one by making use of the Directed Acyclic Word Graph of the pattern. Finally our third algorithm is based on an alignment procedure. We also show that under the assumptions of equiprobability and independence of characters, our second algorithm has a O(n log 2 σ m) average time complexity, for an alphabet of size σ ≥ 4.

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Section: Related Resultsmentioning

confidence: 99%

“…For instance, such mutations are crucial in dna since they often cause genetic diseases [22,23]. For example, large pieces of dna can be moved from one location to another (translocations) [13,25,28,29], or replaced by their reversed complements (inversions) [7].…”

Section: Introductionmentioning

confidence: 99%

Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Cantone,

Faro,

Pavone

2021

Preprint

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“…Regarding the approximate string matching problem, a first solution was presented by Cantone et al [2], where the authors presented an algorithm running in O(nm) worst-case time and O(m 2 )-space for the approximate string matching problem allowing for non-overlapping inversions. Additionally, they also provided a variant [4] of the algorithm which has the same complexity in the worst case, but achieves O(n)-time complexity on average. Cantone et al also proposed in [3] an efficient solution running in O(nm 2 )-time and O(m 2 )space for a slightly more general problem, allowing for balanced translocations of adjacent factors besides non-overlapping inversions.…”

Section: Related Resultsmentioning

confidence: 99%

“…However, evidence shows that in some cases large scale changes are possible [9,20,7] and that such mutations are crucial in dna since they often cause genetic diseases [13,18]. For example, large pieces of dna can be moved from one location to another (translocations) [7,22,21,17], or replaced by their reversed complements (inversions) [4].…”

Section: Introductionmentioning

confidence: 99%

Sequence Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Cantone,

Faro,

Pavone

2018

Preprint

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Unbalanced translocations are among the most frequent chromosomal alterations, accounted for 30% of all losses of heterozygosity, a major genetic event causing inactivation of tumor suppressor genes. Despite of their central role in genomic sequence analysis, little attention has been devoted to the problem of matching sequences allowing for this kind of chromosomal alteration. In this paper we investigate the approximate string matching problem when the edit operations are non-overlapping unbalanced translocations of adjacent factors. In particular, we first present a O(nm 3 )-time and O(m 2 )-space algorithm based on the dynamic-programming approach. Then we improve our first result by designing a second solution which makes use of the Directed Acyclic Word Graph of the pattern. In particular, we show that under the assumptions of equiprobability and independence of characters, our algorithm has a O(n log 2 σ m) average time complexity, for an alphabet of size σ, still maintaining the O(nm 3 )-time and the O(m 2 )-space complexity in the worst case. To the best of our knowledge this is the first solution in literature for the approximate string matching problem allowing for unbalanced translocations of factors.

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“…The distance metric used can be the Hamming distance, the edit distance or other criteria such as the number of non-overlapping inversions (e.g. [4]). In this paper we focus on the Hamming distance.…”

Section: Introductionmentioning

confidence: 99%

On pattern matching with k mismatches and few don't cares

Nicolae

Rajasekaran

2017

Information Processing Letters

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We consider the problem of pattern matching with k mismatches, where there can be don’t care or wild card characters in the pattern. Specifically, given a pattern P of length m and a text T of length n, we want to find all occurrences of P in T that have no more than k mismatches. The pattern can have don’t care characters, which match any character. Without don’t cares, the best known algorithm for pattern matching with k mismatches has a runtime of O(nkthickmathspacelogthickmathspacek). With don’t cares in the pattern, the best deterministic algorithm has a runtime of O(nk polylog m). Therefore, there is an important gap between the versions with and without don’t cares. In this paper we give an algorithm whose runtime increases with the number of don’t cares. We define an island to be a maximal length substring of P that does not contain don’t cares. Let q be the number of islands in P. We present an algorithm that runs in O(nkthickmathspacelogthickmathspacem+nthickmathspacemin{qklog2m3,qlogm}) time. If the number of islands q is O(k) this runtime becomes O(nkthickmathspacelogthickmathspacem), which essentially matches the best known runtime for pattern matching with k mismatches without don’t cares. If the number of islands q is O(k2), this algorithm is asymptotically faster than the previous best algorithm for pattern matching with k mismatches with don’t cares in the pattern.

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Efficient string-matching allowing for non-overlapping inversions

Cited by 24 publications

References 8 publications

Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Sequence Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

On pattern matching with k mismatches and few don't cares

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