Related papers: A simple linear time algorithm for smallest enclos…
We have employed Particle Swarm Optimization to address a stochastic variant of the Smallest Enclosing Sphere estimation problem. An efficient algorithm has been developed to ascertain the optimal center and radius of a sphere encompassing…
Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$…
Given in the plane a set of points and a set of halfplanes, we consider the problem of computing a smallest subset of halfplanes whose union covers all points. In this paper, we present an $O(n^{4/3}\log^{5/3}n\log^{O(1)}\log n)$-time…
In this work we study the minimization problem for the total distance in a cloud computing network on the sphere. We give a solution to this problem in terms of hyperbolic Voronoi diagrams on the sphere. We present results of computer…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
Given a set of $n$ points in the plane, and a parameter $k$, we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing $k$ points. We present the first near quadratic time algorithm for this…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
A linear time algorithm to find a set of nearest elements in a mesh.
In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points…
For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of $n$ points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of…
A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work.…
In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations with a scheduling protocol to further enhance its scalability. Each agent in the network is assumed to…
Given a set $ P $ of $n$ points and a set $ H $ of $n$ half-planes in the plane, we consider the problem of computing a smallest subset of points such that each half-plane contains at least one point of the subset. The previously best…
Clustering objects from the LiDAR point cloud is an important research problem with many applications such as autonomous driving. To meet the real-time requirement, existing research proposed to apply the connected-component-labeling (CCL)…
To date, the best circle graph recognition algorithm runs in almost linear time as it relies on a split decomposition algorithm that uses the union-find data-structure. We show that in the case of circle graphs, the PC-tree data-structure…
Efficient algorithms for solving the Smallest Enclosing Sphere (SES) problem, such as Welzl's algorithm, often fail to handle degenerate subsets of points in 3D space. Degeneracies and ill-posed configurations present significant…
In this paper, we study the problem of computing a minimum-width axis-aligned cubic shell that encloses a given set of $n$ points in a three-dimensional space. A cubic shell is a closed volume between two concentric and face-parallel cubes.…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
In this paper, we present a cluster algorithm for the simulation of hard spheres and related systems. In this algorithm, a copy of the configuration is rotated with respect to a randomly chosen pivot point. The two systems are then…