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Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
Graphics processing units (GPU) had evolved from a specialized hardware capable to render high quality graphics in games to a commodity hardware for effective processing blocks of data in a parallel schema. This evolution is particularly…
We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…
Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
We design, implement, and evaluate GPU-based algorithms for the maximum cardinality matching problem in bipartite graphs. Such algorithms have a variety of applications in computer science, scientific computing, bioinformatics, and other…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…
We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…
We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a…
The Graph Isomorphism (GI) problem is a theoretically interesting problem because it has not been proven to be in P nor to be NP-complete. Babai made a breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI problem.…
In this paper an algorithm is given to determine all possible structurally different linearly conjugate realizations of a given kinetic polynomial system. The solution is based on the iterative search for constrained dense realizations…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…