相关论文: Upper and Lower Bounds on the Cost of a Map-Reduce…

A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this…

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…

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 MapReduce-like distributed computing system. We derive a lower bound on the communication cost for any given storage and computation costs. This lower bound matches the achievable bound we proposed recently. As a result, we…

This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…

A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this…

In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a $3$-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a…

We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query $q$ and the skew in the data, we study tradeoffs between the number of…

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…

The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…

Algorithms have two costs: arithmetic and communication. The latter represents the cost of moving data, either between levels of a memory hierarchy, or between processors over a network. Communication often dominates arithmetic and…

The theme of this paper is how to find all instances of a given "sample" graph in a larger "data graph," using a single round of map-reduce. For the simplest sample graph, the triangle, we improve upon the best known such algorithm. We then…

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…

In the research area of parallel computation, the communication cost has been extensively studied, while the IO cost has been neglected. For big data computation, the assumption that the data fits in main memory no longer holds, and…

This paper presents a reexamination of the research paper titled "Communication-Avoiding Parallel Algorithms for \proc{TRSM}" by Wicky et al. We focus on the communication bandwidth cost analysis presented in the original work and identify…

Distributed processing frameworks, such as MapReduce, Hadoop, and Spark are popular systems for processing large amounts of data. The design of efficient algorithms in these frameworks is a challenging problem, as the systems both require…

We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…

It is well known that load balancing and low delivery communication cost are two critical issues in mapping requests to servers in Content Delivery Networks (CDNs). However, the trade-off between these two performance metrics has not been…

This paper studies the distributed linearly separable computation problem, which is a generalization of many existing distributed computing problems such as distributed gradient descent and distributed linear transform. In this problem, a…