The inability to answer proximity queries efficiently for spaces of dimension d > 2 has led to the study of approximation to proximity problems. Several techniques have been proposed to address different approximate proximity problems. In this paper, we present a new and unified approach to proximity searching, which provides efficient solutions for several problems: spherical range queries, id...

Lemma 2.2. It suffices to find disjoint L,R ∈ V such that they are (1) Large in Ω(n), or more formally stated, |L||R| ≥ α(n). (2) ∆-separated for ∆ = Ω( 1 logn) Let us define what ∆-separated means so that we can formalize this notion of “farness”. Recall that a distance from a vertex i to a set S is defined as d(i, S) = minj∈S d(i, j) (distance to the closest point in the set) and a distance f...

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)...

Graph analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural properties observed over particular representations do not necessarily hold for alternative structures. Because these algorithms tend to be highly effective over ...

When acquiring the surface data of the sample part, it is not easy to get the full data on one scan due to the configuration or topology of the part. In addition, some special parts have special assembly request, for example the joint surface smooth and the boundary share. The process usually requires multiple scans for an assembly model. Some identical points have different coordinate data bec...

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...

In most developing countries children provide some form of insurance against risks when parents are old, which, in turn, justifies parental preference to have more children. In this paper, we examine the causal effect of number of children on several measures of health status of elderly parents using newly available China Health and Retirement Survey data. Because number of children in a family...

Using data from the 2004 Survey of Health, Ageing and Retirement in Europe, this article continues and extends recent cross-national research on proximity and contacts of older parents to their children. In addition to a brief description of the geography of families in 10 continental European countries, determinants of intergenerational proximity and contacts are examined. Even when microlevel...