Related papers: Bidiagonalization with Parallel Tiled Algorithms
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
Iterative algorithms have many advantages for linear tomographic image reconstruction when compared to back-projection based methods. However, iterative methods tend to have significantly higher computational complexity. To overcome this,…
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…
This paper investigates the use of a sampling-based approach, the RRT*, to reconfigure a 2D set of connected tiles in complex environments, where multiple obstacles might be present. Since the target application is automated building of…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
Rapidly-exploring Random Tree star (RRT*) has recently gained immense popularity in the motion planning community as it provides a probabilistically complete and asymptotically optimal solution without requiring the complete information of…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…
An optimal data partitioning in parallel & distributed implementation of clustering algorithms is a necessary computation as it ensures independent task completion, fair distribution, less number of affected points and better & faster…
We propose a new algorithm for binary quantization based on the Belief Propagation algorithm with decimation over factor graphs of Low Density Generator Matrix (LDGM) codes. This algorithm, which we call Bias Propagation (BiP), can be…
The adaptive gradient online learning method known as AdaGrad has seen widespread use in the machine learning community in stochastic and adversarial online learning problems and more recently in deep learning methods. The method's…
This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The…
In this paper, three new dynamic multicast routing algorithms based on the greedy tree technique are proposed; Source Optimised Tree, Topology Based Tree and Minimum Diameter Tree. A simulation analysis is presented showing various…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…