Related papers: On Communication for Distributed Babai Point Compu…
We consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest-plane algorithm, due to Babai.…
We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. We address the problem of reconfiguring a specific rectangular partition, a…
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…
In this paper, we investigate the distributed shortest distance optimization problem for a multi-agent network to cooperatively minimize the sum of the quadratic distances from some convex sets, where each set is only associated with one…
We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of…
A distributed adaptive algorithm to estimate a time-varying signal, measured by a wireless sensor network, is designed and analyzed. One of the major features of the algorithm is that no central coordination among the nodes needs to be…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
In many applications including communications, one may encounter a linear model where the parameter vector $\hbx$ is an integer vector in a box. To estimate $\hbx$, a typical method is to solve a box-constrained integer least squares (BILS)…
We study distributed methods for online prediction and stochastic optimization. Our approach is iterative: in each round nodes first perform local computations and then communicate in order to aggregate information and synchronize their…
Upper bounds on the communication complexity of finding the nearest lattice point in a given lattice $\Lambda \subset \mathbb{R}^2$ was considered in earlier works~\cite{VB:2017}, for a two party, interactive communication model. Here we…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the law of the perturbations, we construct a translation-invariant…
In this paper, we study unconstrained distributed optimization strongly convex problems, in which the exchange of information in the network is captured by a directed graph topology over digital channels that have limited capacity (and…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…
This paper is concerned with detecting an integer parameter vector inside a box from a linear model that is corrupted with a noise vector following the Gaussian distribution. One of the commonly used detectors is the maximum likelihood…