This paper is concerned with a special case of the Generalized Minimum Spanning Tree Problem. The Generalized Minimum Spanning Tree Problem is defined on an undirected graph, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges. The problem is to find a tree of minimum cost containing exactly one vertex in each cluster. We consider a geometric ...

The contour tree is a topological abstraction of a scalar field. It represents the nesting relationships of connected components of isosurfaces or contours. The real-world data sets produce unmanageably large contour trees because of noise and artifacts. This makes the contour tree impractical for data analysis and visualization. A meaningful simplification is necessary to the contour tree. Thi...

Given two sets of points in the plane, P of n terminals and S of m Steiner points, a Steiner tree of P is a tree spanning all points of P and some (or none or all) points of S. A Steiner tree with length of longest edge minimized is called a bottleneck Steiner tree. In this paper, we study the Euclidean bottleneck Steiner tree problem: given two sets, P and S, and a positive integer k ≤ m, find...

In this paper we consider bi-criteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter spanning tree among all possible minimum cost spanning trees, while the latter is to construct a minimum radi...

The Steiner tree problem is to nd the tree with minimal Euclidean length spanning a set of xed points in the plane, given the ability to add points (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an eecient method for computing a locally optimal tree with a given topology. The rst systematically inserts S...

Abstract. 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 intere...

in this study, the effect of hole mulching application of zn and mn on acacia, elm, and plane nutrition was examined in the green spaces of isfahan. three different sites were chosen in a randomized complete block design using six treatments of: 1. cow manure compost, 2. cow manure vermicompost, 3. urban waste compost, 4. urban waste vermicompost, 5. dug hole refilled with the same soil coming ...

For a real number p ≥ 2, an integer k > 0 and a set of terminals X in the plane, the Euclidean power-p Steiner tree problem asks for a tree interconnecting X and at most k Steiner points such that the sum of the p-th powers of the edge lengths is minimised. We show that this problem is in the complexity subclass exp-APX (but not poly-APX) of NPO. We then demonstrate that the approximation algor...

This paper presents the design & analysis of a planar multiband antenna (Iterated Pythagorean fractal tree antenna) with impedance steps in base path. Impedance steps are adopted with finite ground plane for better impedance matching, multiband & bandwidth characteristics as compare to non-iterated form. As tree iteration increases new resonance frequency will obtained, Iterated Pythagorean fra...

We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree T , that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex v ∈ T is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follo...