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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…
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…
Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions. In our model, Alice holds a set of edges and sends a single…
We consider a microgrid where different prosumers exchange energy altogether by the edges of a given network. Each prosumer is located to a node of the network and encompasses energy consumption, energy production and storage capacities…
An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We propose a new construction for low-density source codes with multiple parameters that can be tuned to optimize the performance of the code. In addition, we introduce a set of analysis techniques for deriving upper bounds for the expected…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove an information theoretic lower bound on the number of stochastic gradient queries of the log density needed. Several popular sampling…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Set-disjointness problems are one of the most fundamental problems in communication complexity and have been extensively studied in past decades. Given its importance, many lower bound techniques were introduced to prove communication lower…