We discuss the problem of partitioning a set of points into two subsets with certain conditions on the diameters of the subsets and on their cardinalities. For example, we give an O(n log n) algorithm to find the smallest t such that the set can be split into two equal cardinality subsets each of which has diameter at most t. We also give an algorithm that takes two pairs of points (x, y) and (...

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

BACKGROUND The inferior vena cava (IVC) parameters, including its diameter and collapsibility index have been evaluated for fluid status for over 30 years, but little is known about the impacts of patient characteristics on IVC parameters. The purpose of this study was to explore the relationships between individual patient characteristics and IVC parameters in healthy Chinese adult volunteers....

PURPOSE To evaluate the relationship between the horizontal ciliary sulcus diameter and anterior chamber diameter measured by 35 MHz ultrasound biomicroscopy (UBM) and the horizontal corneal diameter (white to white [WTW]) measured by scanning-slit topography and to assess the repeatability (intraexaminer difference) of the 2 methods. SETTING Department of Orthoptics and Visual Science, Kitas...

carbon spheres were fabricated by hydrothermal method and their structural properties were investigated. carbon spheres with average sizes around of 230, 320 and 430 nm were synthesized in different concentration of glucose aqueous solution and different hydrothermal reaction time. the temperature of 180 °c by a hydrothermal reaction was fixed in all of glucose concentration and hydrothermal re...

the average distance of a vertex $v$ of a connected graph $g$is the arithmetic mean of the distances from $v$ to allother vertices of $g$. the proximity $pi(g)$ and the remoteness $rho(g)$of $g$ are defined as the minimum and maximum averagedistance of the vertices of $g$. in this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tree diameter is useful, for example, in determining an upper bound on the expected number of links bet...

Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation ...