On a non-classical recognition problem

Zenkin, A.I.; Леонтьев, В. К.

doi:10.1016/0041-5553(84)90069-7

Cited by 9 publications

(6 citation statements)

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“…This problem consists of finding the minimum number m=m q (n) such that M m (X ){M m (Z) for any different X, Z # F n q and is far from being conclusive (see [7,8,14,15]). The problems considered belong to the class of metric problems introduced in [12].…”

Section: Discussionmentioning

confidence: 99%

Efficient Reconstruction of Sequences from Their Subsequences or Supersequences

Levenshtein

2001

Journal of Combinatorial Theory, Series A

168

101

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Section: Discussionmentioning

confidence: 99%

Efficient Reconstruction of Sequences from Their Subsequences or Supersequences

Levenshtein

2001

Journal of Combinatorial Theory, Series A

168

101

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“…The problem was first described in [8], where it was also shown that f (n) ⌊n/2⌋. The first lower bounds were established in [19], and improved bounds were described in [9] and [16]. The k-deck problem is also closely related to a number of other reconstruction problems that have received significant attention, such as trace reconstruction [2], reconstruction of graphs from subgraphs [3], and set reconstruction based on multiset information [1].…”

Section: Introductionmentioning

confidence: 99%

The hybrid k-deck problem: Reconstructing sequences from short and long traces

Gabrys

Milenković

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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We introduce a new variant of the k-deck problem, which in its traditional formulation asks for determining the smallest k that allows one to reconstruct any binary sequence of length n from the multiset of its k-length subsequences. In our version of the problem, termed the hybrid k-deck problem, one is given a certain number of special subsequences of the sequence of length n − t, t > 0, and the question of interest is to determine the smallest value of k such that the k-deck, along with the subsequences, allows for reconstructing the original sequence in an error-free manner. We first consider the case that one is given a single subsequence of the sequence of length n − t, obtained by deleting zeros only, and seek the value of k that allows for hybrid reconstruction. We prove that in this case, k ∈ [log t + 2, min{t + 1, O( n · (1 + log t))}]. We then proceed to extend the single-subsequence setup to the case where one is given M subsequences of length n − t obtained by deleting zeroes only. In this case, we first aggregate the asymmetric traces and then invoke the single-trace results. The analysis and problem at hand are motivated by nanopore sequencing problems for DNA-based data storage.

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“…Given the multiset, it is required to determine an unknown word or a set of words whose set of fragments is this multiset. A precise problem setting is as follows [1].…”

Section: Introductionmentioning

confidence: 99%

“…In a number of works this model is known as word reconstruction from fragments [1][2][3][4]. An initial object of analysis is a word.…”

Section: Introductionmentioning

confidence: 99%