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The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and matdot codes are generalized by making use of algebraic…

Information Theory · Computer Science 2024-01-25 Adrián Fidalgo-Díaz , Umberto Martínez-Peñas

In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…

Information Theory · Computer Science 2020-04-14 Qian Yu , A. Salman Avestimehr

Code-based Distributed Matrix Multiplication (DMM) has been extensively studied in distributed computing for efficiently performing large-scale matrix multiplication using coding theoretic techniques. The communication cost and recovery…

Information Theory · Computer Science 2024-08-06 Jiang Li , Songsong Li , Chaoping Xing

A secure multi-party batch matrix multiplication problem (SMBMM) is considered, where the goal is to allow a master to efficiently compute the pairwise products of two batches of massive matrices, by distributing the computation across S…

Information Theory · Computer Science 2020-09-08 Zhen Chen , Zhuqing Jia , Zhiying Wang , Syed A. Jafar

The Gram matrix of a matrix $A$ is defined as $AA^T$ (or $A^T\!A$). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula…

Information Theory · Computer Science 2023-03-10 Okko Makkonen , Camilla Hollanti

We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for minimizing communication costs. The intuition being, that the…

Information Theory · Computer Science 2022-06-10 Roberto Assis Machado , Rafael G. L. D'Oliveira , Salim El Rouayheb , Daniel Heinlein

This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…

Optimization and Control · Mathematics 2020-06-09 Liang Chen , Defeng Sun , Kim-Chuan Toh , Ning Zhang

Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…

Data Structures and Algorithms · Computer Science 2024-06-07 Jean Claude Bajard , Jérémy Marrez , Thomas Plantard , Pascal Véron

We consider the problem of private distributed matrix multiplication under limited resources. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against the workers and…

Information Theory · Computer Science 2021-07-14 Burak Hasircioglu , Jesus Gomez-Vilardebo , Deniz Gunduz

We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i.e., the required number of successful workers. When $m$-th fraction of…

Information Theory · Computer Science 2018-05-17 Sanghamitra Dutta , Mohammad Fahim , Farzin Haddadpour , Haewon Jeong , Viveck Cadambe , Pulkit Grover

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

Information Theory · Computer Science 2019-05-17 Wei-Ting Chang , Ravi Tandon

A popular numerical method to compute SOS (sum of squares of polynomials) decompositions for polynomials is to transform the problem into semi-definite programming (SDP) problems and then solve them by SDP solvers. In this paper, we focus…

Optimization and Control · Mathematics 2015-01-05 Liyun Dai , Bican Xia

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which…

Information Theory · Computer Science 2020-04-10 Qian Yu , Mohammad Ali Maddah-Ali , A. Salman Avestimehr

This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products…

Information Theory · Computer Science 2021-07-21 Jinbao Zhu , Qifa Yan , Xiaohu Tang

In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two…

Information Theory · Computer Science 2023-05-16 Lev Tauz , Lara Dolecek

In nonadaptive combinatorial group testing (CGT), it is desirable to identify a small set of up to $d$ defectives from a large population of $n$ items with as few tests (i.e. large rate) and efficient identifying algorithm as possible. In…

Combinatorics · Mathematics 2020-10-08 Jinping Fan , Hung-Lin Fu , Yujie Gu , Ying Miao , Maiko Shigeno

Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable…

Information Theory · Computer Science 2022-04-19 Xiuxin Tang , Rong Luo

We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of $N$ honest but curious servers under the security constraint that any information…

Information Theory · Computer Science 2022-06-06 Roberto Assis Machado , Felice Manganiello

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

Symbolic Computation · Computer Science 2011-04-06 Changbo Chen , Marc Moreno Maza

This paper has two contributions. First, we propose a novel coded matrix multiplication technique called Generalized PolyDot codes that advances on existing methods for coded matrix multiplication under storage and communication…

Information Theory · Computer Science 2018-11-28 Sanghamitra Dutta , Ziqian Bai , Haewon Jeong , Tze Meng Low , Pulkit Grover