Related papers: Unique Reconstruction of Coded Strings from Multis…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
A weakly constrained code is a collection of finite-length strings over a finite alphabet in which certain substrings or patterns occur according to some prescribed frequencies. Buzaglo and Siegel (ITW 2017) gave a construction of weakly…
The population recovery problem asks one to recover an unknown distribution over $n$-bit strings given access to independent noisy samples of strings drawn from the distribution. Recently, Ban et al. [BCF+19] studied the problem where the…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are…
The insertion-deletion channel takes as input a bit string ${\bf x}\in\{0,1\}^{n}$, and outputs a string where bits have been deleted and inserted independently at random. The trace reconstruction problem is to recover $\bf x$ from many…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up…
Recent experiments have demonstrated the feasibility of storing digital information in macromolecules such as DNA and protein. However, the DNA storage channel is prone to errors such as deletions, insertions, and substitutions. During the…
This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that…
The reconstruction of shredded documents consists of coherently arranging fragments of paper (shreds) to recover the original document(s). A great challenge in computational reconstruction is to properly evaluate the compatibility between…
We study distributed algorithms for string matching problem in presence of wildcard characters. Given a string T (a text), we look for all occurrences of another string P (a pattern) as a substring of string T . Each wildcard character in…
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to…