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In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…
Recurrence equations lie at the heart of many computational paradigms including dynamic programming, graph analysis, and linear solvers. These equations are often expensive to compute and much work has gone into optimizing them for…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected)…
Reliability is an inherent challenge for the emerging nonvolatile technology of racetrack memories, and there exists a fundamental relationship between codes designed for racetrack memories and codes with constrained periodicity. Previous…
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
We study low-complexity iterative decoding algorithms for product codes. We revisit two algorithms recently proposed by the authors based on bounded distance decoding (BDD) of the component codes that improve the performance of conventional…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
A method for designing sequencing barcodes that can withstand a large number of insertion, deletion and substitution errors and are suitable for use in multiplex single-molecule real-time sequencing is presented. The manuscript focuses on…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…
We study the *refuter* problems for proof complexity lower bounds. Suppose $\varphi$ is a hard tautology that does not admit any length-$s$ proof in some proof system $P$. In the corresponding refuter problem, we are given (query access to)…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…