Related papers: A Signature-Based Gr\"obner Basis Algorithm with T…
Nowadays, the notion of semi-regular sequences, originally proposed by Fr\"oberg, becomes very important not only in Mathematics, but also in Information Science, in particular Cryptology. For example, it is highly expected that randomly…
Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their…
$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$.…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
The efficiency of Gr\"obner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on…
Granlund and Montgomery proposed an optimization method for unsigned integer division by constants [3]. Their method (called the GM method in this paper) was further improved in part by works such as [1] and [7], and is now adopted by major…
Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…
Driven by the powerful representation ability of Graph Neural Networks (GNNs), plentiful GNN models have been widely deployed in many real-world applications. Nevertheless, due to distribution disparities between different demographic…
An influential 1990 paper of Hochbaum and Shanthikumar made it common wisdom that "convex separable optimization is not much harder than linear optimization" [JACM 1990]. We exhibit two fundamental classes of mixed integer (linear) programs…
In this paper we state and explain techniques useful for the computation of strong Gr\"obner and standard bases over Euclidean domains: First we investigate several strategies for creating the pair set using an idea by Lichtblau. Then we…
Federated machine learning systems have been widely used to facilitate the joint data analytics across the distributed datasets owned by the different parties that do not trust each others. In this paper, we proposed a novel Gradient…
In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…
Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze…
Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…
Large language models (LLMs) face significant inference latency due to inefficiencies in GEMM operations, weight access, and KV cache access, especially in real-time scenarios. This highlights the need for a versatile compute-memory…
Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…
Integrating multi-omics datasets through data-driven analysis offers a comprehensive understanding of the complex biological processes underlying various diseases, particularly cancer. Graph Neural Networks (GNNs) have recently demonstrated…
Granular ball computing (GBC), as an efficient, robust, and scalable learning method, has become a popular research topic of granular computing. GBC includes two stages: granular ball generation (GBG) and multi-granularity learning based on…
Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…