Related papers: Generalized Unique Reconstruction from Substrings
In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many,…
In this paper, we consider the problem of designing DNA sequences (codewords) for DNA storage systems and DNA computing that are unlikely to fold back onto themselves to form undesirable secondary structures. The paper addresses both the…
Converting a set of sequencing reads into a lossless compact data structure that encodes all the relevant biological information is a major challenge. The classical approaches are to build the string graph or the de Bruijn graph. Each has…
An exact-match overlap graph of $n$ given strings of length $\ell$ is an edge-weighted graph in which each vertex is associated with a string and there is an edge $(x,y)$ of weight $\omega = \ell - |ov_{max}(x,y)|$ if and only if $\omega…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
We present an algorithm for building the extended BWT (eBWT) of a string collection from its grammar-compressed representation. Our technique exploits the string repetitions captured by the grammar to boost the computation of the eBWT.…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
DNA is a leading candidate as the next archival storage media due to its density, durability and sustainability. To read (and write) data DNA storage exploits technology that has been developed over decades to sequence naturally occurring…
We present a framework for the design of optimal assembly algorithms for shotgun sequencing under the criterion of complete reconstruction. We derive a lower bound on the read length and the coverage depth required for reconstruction in…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
In the beautifully simple-to-state problem of trace reconstruction, the goal is to reconstruct an unknown binary string $x$ given random "traces" of $x$ where each trace is generated by deleting each coordinate of $x$ independently with…
Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…
A (tandem) duplication of length $ k $ is an insertion of an exact copy of a substring of length $ k $ next to its original position. This and related types of impairments are of relevance in modeling communication in the presence of…
The first step in any genome assembly algorithm entails the conversion from the domain of strings and overlaps to the language of graphs and paths, typically using one of the two conventional methods: de Bruijn graphs or overlap graphs.…
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
Over the past two decades, a series of works have aimed at studying the problem of genome assembly: the process of reconstructing a genome from sequence reads. An early formulation of the genome assembly problem showed that genome…