相关论文: On the Universality of Round Elimination Fixed Poi…

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with…

This work establishes a novel, unified theoretical framework for a class of high order embedded boundary methods, revealing that the Reconstruction for Off-site Data (ROD) treatment shares a fundamental structure with the recently developed…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…

We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…

Suppose we are given a pair of points $s, t$ and a set $S$ of $n$ geometric objects in the plane, called obstacles. We show that in polynomial time one can construct an auxiliary (multi-)graph $G$ with vertex set $S$ and every edge labeled…

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded…

In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…

Hardness magnification reduces major complexity separations (such as $\mathsf{\mathsf{EXP}} \nsubseteq \mathsf{NC}^1$) to proving lower bounds for some natural problem $Q$ against weak circuit models. Several recent works [OS18, MMW19,…

This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…

We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an…

The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms…

We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…

Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…

Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…