相关论文: Block Korkin-Zolotarev algorithm generalization an…

This article present a parallel CPU implementation of Kannan algorithm for solving shortest vector problem in Block Korkin-Zolotarev lattice reduction method. Implementation based on Native POSIX Thread Library and show linear decrease of…

In article present measure code distance algorithm of binary and ternary linear block code using block Korkin-Zolotarev (BKZ). Proved the upper bound on scaling constant for measure code distance of non-systematic linear block code using…

This article present a application of Block Korkin---Zolotarev lattice reduction method for Lattice Reduction---Aided decoding under MIMO---channel. We give a upper bound estimate on the lattice reduced by block Korkin---Zolotarev method…

The Hermite-Korkine-Zolotarev reduction plays a central role in strong lattice reduction algorithms. By building upon a technique introduced by Ajtai, we show the existence of Hermite-Korkine-Zolotarev reduced bases that are arguably least…

Noisy intermediate-scale quantum cryptanalysis focuses on the capability of near-term quantum devices to solve the mathematical problems underlying cryptography, and serves as a cornerstone for the design of post-quantum cryptographic…

There exist two issues among popular lattice reduction (LR) algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovasz (LLL) algorithms may increase the lengths of basis vectors. The other…

The Korkine-Zolotareff (KZ) reduction has been used in communications and cryptography. In this paper, we modify a very recent KZ reduction algorithm proposed by Zhang et al., resulting in a new algorithm, which can be much faster and more…

This article present a concise estimate of upper and lower bound on the cardinality containing shortest vector in a lattice reduced by block Korkin-Zolotarev method (BKZ) for different value of the block size. Paper show how density affect…

We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR, and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR…

The Korkine-Zolotareff (KZ) reduction is one of the often used reduction strategies for lattice decoding. In this paper, we first investigate some important properties of KZ reduced matrices. Specifically, we present a linear upper bound on…

Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems, and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and…

The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…

This is an English translation of the paper in which N. I. Akhiezer discovered his famous orthogonal polynomials on two intervals in a connection with a generalization of the Korkin-Zolotarev (Korkine-Zolotaref) problem (see the small…

We present an overview of randomized orthogonalization techniques that construct a well-conditioned basis whose sketch is orthonormal. Randomized orthogonalization has recently emerged as a powerful paradigm for reducing the computational…

We explore the use of GPU for accelerating large scale nearest neighbor search and we propose a fast vector-quantization-based exhaustive nearest neighbor search algorithm that can achieve high accuracy without any indexing construction…

We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…

This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…

This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…