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We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform…
Fourier phase retrieval, which seeks to reconstruct a signal from its Fourier magnitude, is of fundamental importance in fields of engineering and science. In this paper, we give a theoretical understanding of algorithms for Fourier phase…
We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
Search is a key service within constraint programming systems, and it demands the restoration of previously accessed states during the exploration of a search tree. Restoration proceeds either bottom-up within the tree to roll back…
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…
The authors of ``A note on the complexity of a phaseless polynomial interpolation'' have shown that phaseless polynomial interpolation over $\mathbf{Q}$ is possible with $n+2$ points, where $n$ is the upper-bound on the degree of a…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
In the pooled data problem the goal is to efficiently reconstruct a binary signal from additive measurements. Given a signal $\sigma \in \{ 0,1 \}^n$, we can query multiple entries at once and get the total number of non-zero entries in the…
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…
We consider a problem which has received considerable attention in systems literature because of its applications to routing in delay tolerant networks and replica placement in distributed storage systems. In abstract terms the problem can…
For many compiled languages, source-level types are erased very early in the compilation process. As a result, further compiler passes may convert type-safe source into type-unsafe machine code. Type-unsafe idioms in the original source and…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
We introduce an optimization-based reconstruction attack capable of completely or near-completely reconstructing a dataset utilized for training a random forest. Notably, our approach relies solely on information readily available in…
Positron emission tomography (PET) is widely used in various clinical applications, including cancer diagnosis, heart disease and neuro disorders. The use of radioactive tracer in PET imaging raises concerns due to the risk of radiation…
Given a multiset of $n$ items from $\mathcal{D}$, the \emph{profile reconstruction} problem is to estimate, for $t = 0, 1, \dots, n$, the fraction $\vec{f}[t]$ of items in $\mathcal{D}$ that appear exactly $t$ times. We consider…
Given a set of integers, one can easily construct the set of their pairwise distances. We consider the inverse problem: given a set of pairwise distances, find the integer set which realizes the pairwise distance set. This problem arises in…
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…
Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…