Related papers: On the Computation Rate of All-Reduce
The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable…
In network function computation is as a means to reduce the required communication flow in terms of number of bits transmitted per source symbol. However, the rate region for the function computation problem in general topologies is an open…
This work explores a distributed computing setting where $K$ nodes are assigned fractions (subtasks) of a computational task in order to perform the computation in parallel. In this setting, a well-known main bottleneck has been the…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
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…
Linear computation broadcast (LCBC) refers to a setting with $d$ dimensional data stored at a central server, where $K$ users, each with some prior linear side-information, wish to retrieve various linear combinations of the data. For each…
The $K$ User Linear Computation Broadcast (LCBC) problem is comprised of $d$ dimensional data (from $\mathbb{F}_q$), that is fully available to a central server, and $K$ users, who require various linear computations of the data, and have…
The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…
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…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
We study network response to queries that require computation of remotely located data and seek to characterize the performance limits in terms of maximum sustainable query rate that can be satisfied. The available resources include (i) a…
We introduce a new technique to certify lower bounds on the multicut size using network coding. In directed networks the network coding rate is not a lower bound on the multicut, but we identify a class of networks on which the rate is…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
I present a model of universal parallel computation called $\Delta$-Nets, and a method to translate $\lambda$-terms into $\Delta$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel…
AllReduce is an important and popular collective communication primitive, which has been widely used in areas such as distributed machine learning and high performance computing. To design, analyze, and choose from various algorithms and…
This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find…