Related papers: A Practical Approach for Computing the Diameter of…
The use of realistic input models has gained popularity in the theory community. Assuming a realistic input model often precludes complicated hypothetical inputs, and the analysis yields bounds that better reflect the behaviour of…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
Geodesic shooting has been successfully applied to diffeo-morphic registration of point sets. Exact computation of the geodesicshooting between point sets, however, requiresO(N2) calculations each time step on the number of points in the…
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…
We present a classical algorithm that, for any $D$-dimensional geometrically-local, quantum circuit $C$ of polylogarithmic-depth, and any bit string $x \in {0,1}^n$, can compute the quantity $|<x|C|0^{\otimes n}>|^2$ to within any…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on projections on C^1 bases and on extreme points of the point process.…
Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) belonging to E denotes the dissimilarity between objects u and v. The diameter of a…
Approximate integer programming is the following: For a convex body $K \subseteq \mathbb{R}^n$, either determine whether $K \cap \mathbb{Z}^n$ is empty, or find an integer point in the convex body scaled by $2$ from its center of gravity…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…