We study the farthest-point distance function, which measures the distance from z ∈ C to the farthest point or points of a given compact set E in the plane. The logarithm of this distance is subharmonic as a function of z, and equals the logarithmic potential of a unique probability measure with unbounded support. This measure σE has many interesting properties that reflect the topology and geo...

Clustering algorithms are routinely used in biomedical disciplines, and are a basic tool in bioinformatics. Depending on the task at hand, there are two most popular options, the central partitional techniques and the Agglomerative Hierarchical Clustering techniques and their derivatives. These methods are well studied and well established. However, both categories have some drawbacks related t...

We systematically investigate the farthest distance function, farthest points, Klee sets, and Chebyshev centers, with respect to Bregman distances induced by Legendre functions. These objects are of considerable interest in Information Geometry and Machine Learning; when the Legendre function is specialized to the energy, one obtains classical notions from Approximation Theory and Convex Analys...

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

This paper presents an alternative to process migration , called competition, to speed up distributed programs in the background on a network of processors. Competition protocols are transparent operating system facilities that involve creating multiple instances (called clones) p 1 , p 2 , etc. of a process P on diier-ent processors, and making clones \compete", i.e., attempting to guarantee t...