Related papers: Communication lower bounds and optimal algorithms …
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…
Load balancing plays a critical role in efficiently dispatching jobs in parallel-server systems such as cloud networks and data centers. A fundamental challenge in the design of load balancing algorithms is to achieve an optimal trade-off…
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…
In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…
In a celebrated work, Blais, Brody, and Matulef developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower…
The Collision problem is to decide whether a given list of numbers $(x_1,\ldots,x_n)\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of them is the case. We show an $n^{\Omega(1)}$ randomised communication lower bound for the natural…
We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…
In decentralized optimization, nodes cooperate to minimize an overall objective function that is the sum (or average) of per-node private objective functions. Algorithms interleave local computations with communication among all or a subset…
Hella et al. (PODC 2012, Distributed Computing 2015) identified seven different models of distributed computing - one of which is the port-numbering model - and provided a complete classification of their computational power relative to…
We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: * high-dimensional…
The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.).…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We prove three new lower bounds for graph connectivity in the $1$-bit broadcast congested clique model, BCC$(1)$. First, in the KT-$0$ version of BCC$(1)$, in which nodes are aware of neighbors only through port numbers, we show an…
In current convolutional neural network (CNN) accelerators, communication (i.e., memory access) dominates the energy consumption. This work provides comprehensive analysis and methodologies to minimize the communication for CNN…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…
In the present paper, we develop the algorithmic correspondence theory for hybrid logic with binder. We define the class of Sahlqvist inequalities, each inequality of which is shown to have a first-order frame correspondent effectively…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…