On reconstructing a string from its substring compositions

Acharya, Jayadev; Das, Hirakendu; Milenković, Olgica; Orlitsky, Alon; Pan, Shilie

doi:10.1109/isit.2010.5513668

Cited by 27 publications

(45 citation statements)

References 4 publications

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“…We say that a string x ∈ {0, 1} n has a nonoverlapping repeated substring of length L − 1 at the positions (i, j), i < j, if x i,L−1 = x j,L−1 and j − i L − 1. For example, the string (1, 0, 1) is a non-overlapping repeated substring of x = (1, 0, 1, 0, 0, 1, 0, 1) at the positions (1,6). On the other hand, if i < j and x i,L−1 = x j,L−1 for j − i < L − 1, we say that x has an overlapping repeated substring of length L − 1 at the positions (i, j).…”

Section: Proofmentioning

confidence: 99%

“…L−1 = 1 and update the last two bits of x (k) to (1,1). If x (k) is (L − 1)-substring unique, set x = x (k) and STOP.…”

Section: Proofmentioning

confidence: 99%

“…Algorithm 2 Encoder E LR for an L-reconstruction code. 1: Let x I ∈ {0, 1} n−2 . If the L − 1 th bit of x I is 1, append (0, 1) to the string.…”

Section: Proofmentioning

confidence: 99%

“…String reconstruction refers to the problem of recovering a string based on some information about its substrings (i.e, strings composed of consecutive elements of the string) or subsequences (i.e, strings composed of possibly non-consecutive elements of the string). Most often, the information is in the form of the sequence spectrum [24], comprising all distinct substrings of the string; the multiset spectrum [17], comprising the multiset of the substrings of the string; the k-deck [22], [31], comprising all subsequences of the string of length k; sequence traces [3], [10], corresponding to randomly selected subsequences of the string; or multiset compositions [1], [2], providing information about the composition of substrings only. The central problem in string reconstruction is to identify which strings may be uniquely reconstructed given a certain substring and subsequence information.…”

Section: Introductionmentioning

confidence: 99%

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Unique Reconstruction of Coded Strings From Multiset Substring Spectra

Gabrys

Milenković

2019

IEEE Trans. Inform. Theory

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The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded string reconstruction from multiset substring spectra, where the strings are restricted to lie in some codebook. In particular, we consider binary codebooks that allow for unique string reconstruction and propose a new method, termed repeat replacement, to create the codebook. Our contributions include algorithmic solutions for repeat replacement and constructive redundancy bounds for the underlying coding schemes. We also consider extensions of the problem to noisy settings in which substrings are compromised by burst and random errors. The study is motivated by applications in DNA-based data storage systems that use high throughput readout sequencers.

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Section: Proofmentioning

confidence: 99%

“…L−1 = 1 and update the last two bits of x (k) to (1,1). If x (k) is (L − 1)-substring unique, set x = x (k) and STOP.…”

Section: Proofmentioning

confidence: 99%

“…Algorithm 2 Encoder E LR for an L-reconstruction code. 1: Let x I ∈ {0, 1} n−2 . If the L − 1 th bit of x I is 1, append (0, 1) to the string.…”

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unique Reconstruction of Coded Strings From Multiset Substring Spectra

Gabrys

Milenković

2019

IEEE Trans. Inform. Theory

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“…Given a finite word w over a finite ordered alphabet Σ, the Parikh vector of w is defined as the vector of multiplicities of the characters in w. In recent years, Parikh vectors have been increasingly studied, in particular Parikh vectors of factors (substrings) of words, motivated by applications in computational biology, e.g. mass spectrometry [1,5,9,10]. Among the new problems introduced in this context is that of jumbled pattern matching (a.k.a.…”

Section: Introductionmentioning

confidence: 99%

On Prefix Normal Words

Fici

Lipták

2011

Developments in Language Theory

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We present a new class of binary words: the prefix normal words. They are defined by the property that for any given length k, no factor of length k has more a's than the prefix of the same length. These words arise in the context of indexing for jumbled pattern matching (a.k.a. permutation matching or Parikh vector matching), where the aim is to decide whether a string has a factor with a given multiplicity of characters, i.e., with a given Parikh vector. Using prefix normal words, we give the first non-trivial characterization of binary words having the same set of Parikh vectors of factors. We prove that the language of prefix normal words is not context-free and is strictly contained in the language of pre-necklaces, which are prefixes of powers of Lyndon words. We discuss further properties and state open problems.

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Semi-supervised time series classification method for quantum computing

Yarkoni

Kleshchonok

Dzerin

et al. 2021

Quantum Mach. Intell.

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In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.

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On reconstructing a string from its substring compositions

Cited by 27 publications

References 4 publications

Unique Reconstruction of Coded Strings From Multiset Substring Spectra

Unique Reconstruction of Coded Strings From Multiset Substring Spectra

On Prefix Normal Words

Semi-supervised time series classification method for quantum computing

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