Cluster connecting problem inside a polygon
نویسندگان
چکیده
The cluster connecting problem inside a simple polygon is introduced in this paper. The problem is shown to be NP-complete. A logn-factor approximation algorithm is proposed.
منابع مشابه
Jim Stewart 1 Shortest Path Problems
The topic of this lecture is the application of triangulations to shortest path problems. Only simple polygons will be considered. Given two points inside a polygon, the goal is to find the shortest path lying inside the polygon between the two points; see Fig. 1. One can think of the shortest path as a taut string connecting the two points. We begin with some definitions. Let P be a simple pol...
متن کاملSelf-Approaching Paths in Simple Polygons
We study self-approaching paths that are contained in a simple polygon. A self-approaching path is a directed curve connecting two points such that the Euclidean distance between a point moving along the path and any future position does not increase, that is, for all points a, b, and c that appear in that order along the curve, |ac| ≥ |bc|. We analyze the properties, and present a characteriza...
متن کاملCreating Polygon Models for Spatial Clusters
This paper proposes a novel methodology for creating efficient polygon models for spatial datasets. A comprehensive analysis framework is proposed that takes a spatial cluster as an input and generates a polygon model for the cluster as an output. The framework creates a visually appealing, simple, and smooth polygon for the cluster by minimizing a fitness function. We propose a novel polygon f...
متن کاملSpeed-constrained geodesic fréchet distance inside a simple polygon
Given two polygonal curves inside a simple polygon, we study the problem of finding the Fréchet distance between the two curves under the following two conditions (i) the distance between two points on the curves is measured as the length of the shortest path between them lying inside the simple polygon, and (ii) the traversal along each segment of the polygonal curves is restricted to be betwe...
متن کاملThe Complexity of Guarding Monotone Polygons
A polygon P is x-monotone if any line orthogonal to the x-axis has a simply connected intersection with P . A set G of points inside P or on the boundary of P is said to guard the polygon if every point inside P or on the boundary of P is seen by a point in G. An interior guard can lie anywhere inside or on the boundary of the polygon. Using a reduction fromMonotone 3SAT, we prove that interior...
متن کامل