Given in the plane a set S of m point sites simple polygon P n vertices, we consider problem computing geodesic farthest-point Voronoi diagram for P. It is known that has an $$\Omega (n+m\log m)$$ time lower bound. Previously, randomized algorithm was proposed [Barba, SoCG 2019] solves $$O(n+m\log expected time. The previous best deterministic algorithms solve $$O(n\log \log n+ m\log [Oh, Barba...

The k-modes algorithm has become a popular technique in solving categorical data clustering problems in different application domains. However, the algorithm requires random selection of initial points for the clusters. Different initial points often lead to considerable distinct clustering results. In this paper we present an experimental study on applying a farthest-point heuristic based init...

A new method of farthest point strategy (FPS) for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FP...

Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce optimal data structures supporting queries for the farthest di...

In an earlier paper, we briefly presented a new halftoning algorithm called farthest-point halftoning. In the present paper, this method is analyzed in detail, and a novel dispersion measure is defined to improve the simplicity and flexibility of the result. This new stochastic screen algorithm is loosely based on Kang’s dispersed-dot ordered dither halftone array construction technique used as...

In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n logn) algorithm for the following proximity problem: Given a set P of n (>2) points in the plane, we have O(n2) implicitly defined segments on pairs of points. For each point p ∈ P , find a segment from this set of implicitly defined segment...

We present an algorithm that computes the diameter of a set of n points in the cylinder in optimal time O(n log n); this algorithm uses as a fundamental tool the farthest point Voronoi diagram.

Can one walk to infinity on Gaussian primes taking steps of bounded length?” We adopted computational techniques to probe into this open problem. We propose an efficient method to search for the farthest point reachable from the origin, which can be parallelized easily, and have confirmed the existence of a moat of width k = √ 36, whereas the best previous result was k = √ 26 due to Gethner et ...

In this project, we study proximity problems in high dimensional space. We give efficient algorithms in the data stream model that compute an approximation of the Minimum Enclosing Ball and diameter of a point set. We also give a simple insertion only data sructure that answers approximate farthest point queries.

An earlier result states that a point of the surface of a convex polyhedron with n vertices, endowed with its intrinsic metric, cannot have more than n antipodes (farthest points). In this paper we produce examples of polyhedra with n vertices, on which some suitable point admits exactly n antipodes. MSC (2000): 52B10, 53C45.