Related papers: Parallel parametric linear programming solving, an…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
The generalized method to have a parallel solution to a computational problem, is to find a way to use Divide & Conquer paradigm in order to have processors acting on its own data and therefore all can be scheduled in parallel. MapReduce is…
What is a systematic way to efficiently apply a wide spectrum of advanced ML programs to industrial scale problems, using Big Models (up to 100s of billions of parameters) on Big Data (up to terabytes or petabytes)? Modern parallelization…
Multicore parallel programming has some very difficult problems such as deadlocks during synchronizations and race conditions brought by concurrency. Added to the difficulty is the lack of a simple, well-accepted computing model for…
Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of…
In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
The symbolic manipulation program FORM is specialized to handle very large algebraic expressions. Some specific features of its internal structure make FORM very well suited for parallelization. We have now two parallel versions of FORM,…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
We consider parametric linear programming problems with multiple objective functions depending linearly on some parameter. Both parametric (single-objective) linear programming and (non-parametric) multi-objective linear programming are…
The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In particular, pretropisms are candidate leading exponents for the…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
The advent of high performance computing (HPC) and graphics processing units (GPU), present an enormous computation resource for Large data transactions (big data) that require parallel processing for robust and prompt data analysis. While…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…