Related papers: A New Fast Computation of a Permanent
We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A…
Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear…
Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users' local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
We show that there is a polynomial space algorithm that counts the number of perfect matchings in an $n$-vertex graph in $O^*(2^{n/2})\subset O(1.415^n)$ time. ($O^*(f(n))$ suppresses functions polylogarithmic in $f(n)$).The previously…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
Matrix multiplication $A^t A$ appears as intermediate operation during the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm for the $A^t A$ multiplication. Our algorithm, A$\scriptstyle…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
This note presents fast Cholesky/LU/QR decomposition algorithms with $O(n^{2.529})$ time complexity when using the fastest known matrix multiplication. The algorithms have potential application, since a quickly made implementation using…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of…
We revisit the problem of permuting an array of length $n$ according to a given permutation in place, that is, using only a small number of bits of extra storage. Fich, Munro and Poblete [FOCS 1990, SICOMP 1995] obtained an elegant…
A linear-complexity algorithm for computing the Wasserstein-1 distance on non-uniform meshes is proposed. This work extends the fast Sinkhorn algorithms from [Q. Liao et al., Commun. Math. Sci., 20(2022)] and [Q. Liao et al., J. Sci.…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…
In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using…
Frequent Pattern Mining is a one field of the most significant topics in data mining. In recent years, many algorithms have been proposed for mining frequent itemsets. A new algorithm has been presented for mining frequent itemsets based on…
In the recent publication (arxiv:2007.08063v2 [cs.LG]) a fast prediction algorithm for a single recurrent network (RN) was suggested. In this manuscript we generalize this approach to a chain of RNs and show that it can be implemented in…