Related papers: Geometric Algorithms with Limited Workspace: A Sur…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. However, it remains unclear what aspects of neural activity contribute to these computational…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
In this paper we present new algorithmic solutions for several constrained geometric server placement problems. We consider the problems of computing the 1-center and obnoxious 1-center of a set of line segments, constrained to lie on a…
Design space exploration is commonly performed in embedded system, where the architecture is a complicated piece of engineering. With the current trend of many-core systems, design space exploration in general-purpose computers can no…
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…
Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
The aim of the paper is to show algorithms for geometrical manipulations on NURBS surfaces. These include generating NURBS surfaces that pass through given points, calculating the minimum distance to a point and include line to surface and…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
Constant workspace algorithms use a constant number of words in addition to the read-only input to the algorithm. In this paper, we devise algorithms to efficiently compute relative hulls in the plane using a constant workspace.…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
We consider the problem of scheduling a set of $n$ tasks on $m$ processors under precedence, communication, and global system energy constraints to minimize makespan. We extend existing scheduling models to account for energy usage and give…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
For many computational problems involving randomness, intricate geometric features of the solution space have been used to rigorously rule out powerful classes of algorithms. This is often accomplished through the lens of the multi Overlap…
In this paper, we present an advanced analysis of near optimal algorithms that use limited space to solve the frequency estimation, heavy hitters, frequent items, and top-k approximation in the bounded deletion model. We define the family…
We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…