相关论文: Ability to Count Is Worth $\Theta(\Delta)$ Rounds

In this paper, we revisit the communication vs. distributed computing trade-off, studied within the framework of MapReduce in [1]. An implicit assumption in the aforementioned work is that each server performs all possible computations on…

We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…

We consider the LOCAL model of distributed computing, where in a single round of communication each node can send to each of its neighbors a message of an arbitrary size. It is know that, classically, the round complexity of 3-coloring an…

We consider distributed online learning protocols that control the exchange of information between local learners in a round-based learning scenario. The learning performance of such a protocol is intuitively optimal if approximately the…

In the last few years, the theory of decentralized distributed convex optimization has made significant progress. The lower bounds on communications rounds and oracle calls have appeared, as well as methods that reach both of these bounds.…

Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this…

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

We consider a number of fundamental statistical and graph problems in the message-passing model, where we have $k$ machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…

We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…

Consider a computer network that consists of a path with $n$ nodes. The nodes are labeled with inputs from a constant-sized set, and the task is to find output labels from a constant-sized set subject to some local constraints---more…

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…

We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of…

The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only…

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with…

We consider a distributed computing framework where the distributed nodes have different communication capabilities, motivated by the heterogeneous networks in data centers and mobile edge computing systems. Following the structure of…

In this paper we study the tradeoff between parallelism and communication cost in a map-reduce computation. For any problem that is not "embarrassingly parallel," the finer we partition the work of the reducers so that more parallelism can…

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…