منابع مشابه
Short trees in polygons
We consider the problem of determining the shortest Euclidean tree for terminals in a simple polygon. We give a fast polynomial heuristic based on greedy concatenation of Euclidean Steiner minimal trees with up to four terminals. Computational results indicate that the solutions obtained are close to optimal solutions. Another important contribution of the paper are linear time algorithms for o...
متن کاملTrees in simple Polygons
We prove that every simple polygon contains a degree 3 tree encompassing a prescribed set of vertices. We give tight bounds on the minimal number of degree 3 vertices. We apply this result to reprove a result from Bose et al. [3] that every set of disjoint line segments in the plane admits a binary tree. Introduction Recently many papers have been published regarding the augmentation of discret...
متن کاملSteiner Minimal Trees in Simple Polygons
An O(n log n) time and O(n) space algorithm for the Euclidean Steiner tree problem with four terminals in a simple polygon with n vertices is given. Its applicability to the problem of determining good quality solutions for any number of terminals is discussed.
متن کاملOn Unfolding Lattice Polygons/Trees and Diameter-4 Trees
We consider the problems of straightening polygonal trees and convexifying polygons by continuous motions such that rigid edges can rotate around vertex joints and no edge crossings are allowed. A tree can be straightened if all its edges can be aligned along a common straight line such that each edge points “away” from a designated leaf node. A polygon can be convexified if it can be reconfigu...
متن کاملCellular Structures Determined by Polygons and Trees
The polytope structure of the associahedron is decomposed into two categories, types and classes. The classification of types is related to integer partitions, whereas the classes present a new combinatorial problem. We solve this, generalizing the work of [25], and incorporate the results into properties of the moduli space Mn 0 (R) studied in [8]. Connections are discussed with relation to cl...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2002
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(01)00256-6