: We give a tight analysis of an old and popular sweep-line heuristic for constructing a spanning tree of a set of n points in the plane. The algorithm sweeps a vertical line acros...
Abstract: This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover whe...
Vladimir Estivill-Castro, Apichat Heednacram, Fran...
For an integer n 3, a rank-n matroid is called an n-spike if it consists of n three-point lines through a common point such that, for all k {1, 2, . . . , n - 1}, the union of e...
Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted li...
In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficie...