Approximate pattern matching on elastic-degenerate text

Bernardini, Giulia; Pisanti, Nadia; Pissis, Solon P.; Rosone, Giovanna

doi:10.1016/j.tcs.2019.08.012

Cited by 18 publications

(14 citation statements)

References 22 publications

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“…We leave it as open question if similar solutions can be derived for arbitrary DAGs, or e.g. for elastic degenerate strings [5]. Or more generally, can bit-parallel algorithms with more complex dependencies, like in the case of approximate pattern matching, be turned into quantum algorithms?…”

Section: Discussionmentioning

confidence: 99%

Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model

Equi¹,

Meijer-van²,

Mäkinen³

2021

Preprint

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Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor w, where w is the computer word size. For example, edit distance of two strings of length n can be solved in O(n 2 /w) time. In a reasonable classical model of computation, one can assume w = Θ(log n). There are conditional lower bounds for such problems stating that speedups with factor n for any > 0 would lead to breakthroughs in complexity theory. However, these conditional lower bounds do not cover quantum models of computing. Moreover, it is open if problems like edit distance can be solved in truly sub-quadratic time using quantum computing. To partially address this question, we study another bit-parallel algorithm for a problem that admits a quadratic conditional lower bound, and show how to convert its bit-parallelism into a realistic quantum algorithm that attains speed-up with factor n. The technique we use is simple and general enough to apply to many similar bit-parallel algorithms, where dependencies are local. However, it does not immediately yield a faster algorithm for more complex problems like edit distance, whose bit-parallel dynamic programming solutions require breaking more global dependencies. We hope that this initial study sheds some light on how, in general, bit-parallelism could be converted to quantum parallelism.

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Section: Discussionmentioning

confidence: 99%

Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model

Equi¹,

Meijer-van²,

Mäkinen³

2021

Preprint

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show abstract

“…An elastic-degenerate string is a sequence of sets of strings used for succinctly representing a multiple alignment of a collection of closely related sequences (e.g. a pan-genome, that is all genes and genetic variation within a species), and also supports approximate pattern matching [4]. Sequence alignment is useful for inferring evolutionary relationships between biological sequences.…”

Section: Applications On Meta Stringsmentioning

confidence: 99%

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Daykin,

Köppl,

Kübel

et al. 2021

Preprint

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We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the respective string length. We show that an arithmetically progressed permutation P coincides with the suffix array of a unary, binary, or ternary string. We further analyze the conditions of a given P under which we can find a uniquely defined string over either a binary or ternary alphabet having P as its suffix array. For the binary case, we show its connection to lower Christoffel words, balanced words, and Fibonacci words. In addition to solving the arithmetically progressed suffix array problem, we give the shape of the Burrows-Wheeler transform of those strings solving this problem. These results give rise to numerous future research directions.

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“…That is, any set ofS does not contain, in general, only single letters, nor substrings of the same length, as it may contain strings of different lengths, including the empty string (see Figure 1). In a few recent papers, several algorithms for pattern matching on ED strings have been presented; specifically, for finding all exact [8,10,11,12,13] or approximate [14,15] occurrences of a standard string pattern in an ED text.…”

Section: And References Therein)mentioning

confidence: 99%

Comparing Degenerate Strings

Alzamel

Ayad

Bernardini

et al. 2020

Self Cite

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Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string Ŝ is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1, . . . , kn-1. Our main result is an 𝒪(N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in Ŝ in 𝒪(min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in Ŝ. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach.

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Approximate pattern matching on elastic-degenerate text

Cited by 18 publications

References 22 publications

Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model

Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Comparing Degenerate Strings

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