Related papers: Near-Optimal Average-Case Approximate Trace Recons…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
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…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we…
We consider the problem of reconstructing an undirected graph $G$ on $n$ vertices given multiple random noisy subgraphs or "traces". Specifically, a trace is generated by sampling each vertex with probability $p_v$, then taking the…
The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by deletions, insertions, and substitutions. This problem arises in applications such as DNA data storage, a…
Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…
We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense…
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…
The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use…
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…
We show that any $n$-bit string can be recovered with high probability from $\exp(\widetilde{O}(n^{1/5}))$ independent random subsequences.
We study approximation algorithms for variants of the \emph{median string} problem, which asks for a string that minimizes the sum of edit distances from a given set of $m$ strings of length $n$. Only the straightforward $2$-approximation…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
The problem of reconstructing a string from its error-prone copies, the trace reconstruction problem, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction,…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…