Journal ArticleDOI
Communication complexity of matrix computation over finite fields
Jeff I. Chu,Georg Schnitger +1 more
TLDR
It is shown that, forn×n matrices whose entries are elements of a finite field of sizep, the communication complexity of this problem is Θ(n2 logp), which implies tight bounds for several other problems liked determining the rank and computing the determinant.Abstract:
We investigate the communication complexity of singularity testing in a finite field, where the problem is to determine whether a given square matrixM is singular. We show that, forn×n matrices whose entries are elements of a finite field of sizep, the communication complexity of this problem is Θ(n2 logp). Our results imply tight bounds for several other problems likedetermining the rank andcomputing the determinant.read more
Citations
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Proceedings ArticleDOI
Numerical linear algebra in the streaming model
TL;DR: Near-optimal space bounds are given in the streaming model for linear algebra problems that include estimation of matrix products, linear regression, low-rank approximation, and approximation of matrix rank; results for turnstile updates are proved.
Book ChapterDOI
Further Algebraic Algorithms in the Congested Clique Model and Applications to Graph-Theoretic Problems
TL;DR: Deterministic and randomized algorithms are presented, in the congested clique model, for efficiently computing multiple independent instances of matrix products, computing the determinant, the rank and the inverse of a matrix, and solving systems of linear equations.
Proceedings ArticleDOI
Randomized Communication Complexity for Linear Algebra Problems over Finite Fields
Xiaoming Sun,Chengu Wang +1 more
TL;DR: It is proved that the randomized/quantum communication complexity of the singularity problem over F_p is Omega(n^2 log p), which implies the same space lower bound for randomized streaming algorithms, even for a constant number of passes.
Proceedings Article
Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds
TL;DR: In this paper, the authors studied the problem of estimating the number of eigenvalues that are greater than a constant in a distributed setting, where the matrix of interest is the sum of m matrices held by separate machines, and showed that any deterministic algorithm solving this problem must communicate Ω(n 2 ) bits, which is order equivalent to transmitting the whole matrix.
Book ChapterDOI
On the Communication Complexity of Linear Algebraic Problems in the Message Passing Model
TL;DR: In this article, the authors studied the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, and proved a number of tight lower bounds.
References
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Proceedings ArticleDOI
Some complexity questions related to distributive computing(Preliminary Report)
TL;DR: The quantity of interest, which measures the information exchange necessary for computing f, is the minimum number of bits exchanged in any algorithm.
Proceedings Article
Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity (Extended Abstract)
Benny Chor,Oded Goldreich +1 more
TL;DR: In this article, a new model for weak random physical sources is presented, which strictly generalizes previous models (e.g., the Santha and Vazirani model [27]).
Proceedings ArticleDOI
Area-time complexity for VLSI
TL;DR: The complexity of the Discrete Fourier Transform is studied with respect to a new model of computation appropriate to VLSI technology, which focuses on two key parameters, the amount of silicon area and time required to implement a DFT on a single chip.
Journal ArticleDOI
The fast Fourier transform in a finite field
TL;DR: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the Fast Fourier Transform (FFT) algorithm as discussed by the authors.