相关论文: Reconstruction of multiple strings of constant wei…

Motivated by applications in polymer-based data storage, we study the problem of reconstructing a string from part of its composition multiset. We give a full description of the structure of the strings that cannot be uniquely reconstructed…

The problem of string reconstruction from substring information has found many applications due to its relevance in DNA- and polymer-based data storage. One practically important and challenging paradigm requires reconstructing mixtures of…

The problem of reconstructing strings from substring information has found many applications due to its importance in genomic data sequencing and DNA- and polymer-based data storage. One practically important and challenging paradigm…

The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all…

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm…

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…

Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for unique string…

Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for both unique string…

Synthetic polymer-based storage seems to be a particularly promising candidate that could help to cope with the ever-increasing demand for archival storage requirements. It involves designing molecules of distinct masses to represent the…

We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…

This paper studies reconstruction of strings based upon their substrings spectrum. Under this paradigm, it is assumed that all substrings of some fixed length are received and the goal is to reconstruct the string. While many existing works…

The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…

Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…

This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…

Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length…

A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…

Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…

In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…