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The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…
Given an approximation algorithm $A$, we want to find the input with the worst approximation ratio, i.e., the input for which $A$'s output's objective value is the worst possible compared to the optimal solution's objective value. Such hard…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
Probabilistic Circuits (PCs) offer a computationally scalable framework for generative modeling, supporting exact and efficient inference of a wide range of probabilistic queries. While recent advances have significantly improved the…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…
In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…
We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…
This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been…
Protein/Peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and highthroughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having…
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,…
Due to the falling costs of data acquisition and storage, researchers and industry analysts often want to find all instances of rare events in large datasets. For instance, scientists can cheaply capture thousands of hours of video, but are…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…
Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the…