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Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the…
Dense, discrete Graphical Models with pairwise potentials are a powerful class of models which are employed in state-of-the-art computer vision and bio-imaging applications. This work introduces a new MAP-solver, based on the popular Dual…
The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…
The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…
Most, if not all the modern scientific simulation packages utilize matrix algebra operations. Among the operation of the linear algebra, one of the most important kernels is the multiplication of matrices, dense and sparse. Examples of…
Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its…
Linear Programs (LPs) appear in a large number of applications and offloading them to a GPU is viable to gain performance. Existing work on offloading and solving an LP on a GPU suggests that there is performance gain generally on large…
In this paper, a new graph partitioning problem is introduced. The depth of each part is constrained, i.e., the node count in the longest path of the corresponding sub-graph is no more than a predetermined positive integer value p. An…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…
The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing…
In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry,…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
Large industrial systems that combine services and applications, have become targets for cyber criminals and are challenging from the security, monitoring and auditing perspectives. Security log analysis is a key step for uncovering…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…
Clustering is an important tool in data analysis, with K-means being popular for its simplicity and versatility. However, it cannot handle non-linearly separable clusters. Kernel K-means addresses this limitation but requires a large kernel…
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…