Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane bounded by a simple polygon and a free tree, we show that deciding whether there is a planar straight-line embedding of the tree on the point set inside the...

We are given a set P of points in the plane, together with a partition of P into classes of points; i.e., each point of P belongs to exactly one class. For a given network optimization problem, such as nding a minimum spanning tree or nding a minimum diameter spanning tree, we study the problem of choosing a subset P 0 of P that contains at least one point of each class and solving the network ...

Data are presented on the effect of the tree canopy transmittance in the visible waveband (VT), canopy width, height and height of the start of the tree canopy (CH) on the solar UV in tree shade on a horizontal plane at ground level during a Southern Hemisphere summer. Of these factors, the VT and CH have an influence on the UV irradiances in the tree shade. The shade ratios (UV in tree shade t...

Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i.e., labellings of the nodes by distinct integers of the set {1, . . . , n} in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recurs...

Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( √ n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more general setting), point at some methods for constructing such a tree, and describe some algorithmic...

This paper presents a design method of on-chip patch antenna integration in a standard CMOS technology without post processing. A 60 GHz on-chip patch antenna is designed utilizing the top metal layer and an intermediate metal layer as the patch and ground plane, respectively. Interference between the patch and digital baseband circuits located beneath the ground plane is analyzed. The 60 GHz o...

The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrary metric and 1.267 in rec...

A non-crossing tree (NC-tree) is a tree drawn on the plane having as vertices a set of points on the boundary of a circle, and whose edges are straight line segments that do not cross. In this paper, we show that NC-trees with size n are conditioned Galton–Watson trees. As corollaries, we give the limit law of depth-first traversal processes and the limit profile of NC-trees.

The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrary metric and 1.267 in rec...

An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. We give an O(n logn) algorithm to compute the e...