Related papers: Quality Up in Polynomial Homotopy Continuation by …
Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy…
In high performance computing environments, we observe an ongoing increase in the available numbers of cores. This development calls for re-emphasizing performance (scalability) analysis and speedup laws as suggested in the literature…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…
We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach based on a parametric variant of the Krawczyk method from…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…
Multiple string matching is known as locating all the occurrences of a given number of patterns in an arbitrary string. It is used in bio-computing applications where the algorithms are commonly used for retrieval of information such as…
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy based solvers in terms of decorated graphs. Under the…
The aim of parallel computing is to increase an application performance by executing the application on multiple processors. OpenMP is an API that supports multi platform shared memory programming model and shared-memory programs are…
We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the…
Fault tolerance overhead of high performance computing (HPC) applications is becoming critical to the efficient utilization of HPC systems at large scale. HPC applications typically tolerate fail-stop failures by checkpointing. Another…
Modularity is one of the most widely used quality measures for graph clusterings. Maximizing modularity is NP-hard, and the runtime of exact algorithms is prohibitive for large graphs. A simple and effective class of heuristics coarsens the…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
Multicore architectures dominate today's processor market. Even though the number of cores and threads are pretty high and continues to grow, inherently serial algorithms do not benefit from the abundance of cores and threads. In this…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
The goal of this paper is to study the path-following method for univariate polynomials. We propose to study the complexity and condition properties when the Newton method is applied as a correction operator. Then we study the geodesics and…
The overwhelmingly increasing amount of stored data has spurred researchers seeking different methods in order to optimally take advantage of it which mostly have faced a response time problem as a result of this enormous size of data. Most…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…