Related papers: How good is the Chord algorithm?
Online averaged stochastic gradient algorithms are more and more studied since (i) they can deal quickly with large sample taking values in high dimensional spaces, (ii) they enable to treat data sequentially, (iii) they are known to be…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors,…
Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. In this work, we consider a well-studied quantum algorithm for combinatorial optimization: the Quantum Approximate…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
Chord diagrams are used by guitar players to show where and how to play a chord on the fretboard. They are useful to beginners learning chords or for sharing the hand positions required to play a song.However, the diagrams presented on…
We present an approximation algorithm for computing the diameter of a point-set in $\Re^d$. The new algorithm is sensitive to the ``hardness'' of computing the diameter of the given input, and for most inputs it is able to compute the exact…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Identifying a preferable route is an important problem that finds applications in map services. When a user plans a trip within a city, the user may want to find "a most popular route such that it passes by shopping mall, restaurant, and…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…