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...

This short note describes a development of the traditional Pythagorean tree fractal to produce interesting three-dimensional structures based on cubes rather than squares. Adding a 90˚rotation at each bifurcation encourages three-dimensional growth, creating increasingly artistic shapes as the branching angle decreases. 1. Pythagorean box trees The Pythagorean tree is a plane fractal constructe...

We present worst-case lower bounds on the minimum size of a binary space partition (BSP) tree as a function of its height, for a set S of n axis-parallel line segments in the plane. We assume that the BSP uses only axis-parallel cutting lines. These lower bounds imply that, in the worst case, a BSP tree of height O(log n) must have size Ω(n logn) and a BSP tree of size O(n) must have height Ω(n...

In this paper, we study a Steiner tree related problem called “Terminal Steiner Tree with Bounded Edge Length”: given a set of terminal points P in a plane, one is asked to find a Steiner tree T such that any point in P is a leaf in T and the length of each edge in T is no more than a constant b. The objective of the problem is to minimize the number of Steiner points in T . This problem is mot...

We introduce a new BSP tree construction method for set of segments in the plane. Our algorithm is able to create BSP tree of linear size in the time O(n log n) for set of segments with low directional density (i.e. it holds for arbitrary segment si from such set, that a line created as extension of this segment doesn’t intersect too many other segments from the set in a near neighbourhood of s...