Related papers: Parity-Checked Strassen Algorithm
In distributed computing systems, it is well recognized that worker nodes that are slow (called stragglers) tend to dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of…
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for the computations at the agents is affected by the availability of local resources…
In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as a means to bound the exponent $\omega$ of matrix…
In the sparse polynomial multiplication problem, one is asked to multiply two sparse polynomials f and g in time that is proportional to the size of the input plus the size of the output. The polynomials are given via lists of their…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
In response to a recent Nature article which announced an algorithm for multiplying $5\times5$-matrices over $\mathbb{Z}_2$ with only 96 multiplications, two fewer than the previous record, we present an algorithm that does the job with…
The multiplicity Schwartz-Zippel lemma asserts that over a field, a low-degree polynomial cannot vanish with high multiplicity very often on a sufficiently large product set. Since its discovery in a work of Dvir, Kopparty, Saraf and Sudan…
Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \times n$ square matrices combining ``\emph{Strassen-like}'' fast matrix multiplication approach with…
We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs executed before a common due date. By preprocessing and constructing an auxiliary…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint…
Initiated by Mulmuley, Vazirani, and Vazirani (1987), many algebraic algorithms have been developed for matching and related problems. In this paper, we review basic facts and discuss possible improvements with the aid of fast computation…
The Strassen $2\times2$ matrix multiplication algorithm arises from the volume form on the 3-dimensional quotient space of the $2\times 2$ matrices by the multiples of identity.
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
We present several polynomial- and quasipolynomial-time approximation schemes for a large class of generalized operator norms. Special cases include the $2\rightarrow q$ norm of matrices for $q>2$, the support function of the set of…
Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
Two-sided matching platforms provide users with menus of match recommendations. To maximize the number of realized matches between the two sides (referred here as customers and suppliers), the platform must balance the inherent tension…
In this paper, due to the important value in practical applications, we consider the coded distributed matrix multiplication problem of computing $AA^\top$ in a distributed computing system with $N$ worker nodes and a master node, where the…