Vertex Guards in a Subclass of Orthogonal Polygons
نویسندگان
چکیده
We call grid n-ogon each n-vertex orthogonal simple polygon, with no collinear edges, that may be placed in a ) 2 / ( ) 2 / ( n n × unit square grid. In this paper we consider the Minimum Vertex Guard problem for this class of orthogonal polygons. As a step for the resolution of this general problem, we are going to study it for an interesting subclass of grid n-ogons: the SPIRAL grid nogons, which are the grid n-ogons whose boundary can be divided into a reflex chain and a convex chain.
منابع مشابه
A Fast Algorithm for Covering Rectangular Orthogonal Polygons with a Minimum Number of r-Stars
Introduction This paper presents an algorithm for covering orthogonal polygons with minimal number of guards. This idea examines the minimum number of guards for orthogonal simple polygons (without holes) for all scenarios and can also find a rectangular area for each guards. We consider the problem of covering orthogonal polygons with a minimum number of r-stars. In each orthogonal polygon P,...
متن کاملOrthogonal Art Galleries with Holes: A Coloring Proof of Aggarwal's Theorem
We prove that bn+h 4 c vertex guards are always sufficient to see the entire interior of an n-vertex orthogonal polygon P with an arbitrary number h of holes provided that there exists a quadrilateralization whose dual graph is a cactus. Our proof is based upon 4-coloring of a quadrilateralization graph, and it is similar to that of Kahn and others for orthogonal polygons without holes. Consequ...
متن کاملOptimizing the Minimum Vertex Guard Set on Simple Polygons via a Genetic Algorithm
The problem of minimizing the number of vertex-guards necessary to cover a given simple polygon (MINIMUM VERTEX GUARD (MVG) problem) is NP-hard. This computational complexity opens two lines of investigation: the development of algorithms that establish approximate solutions and the determination of optimal solutions for special classes of simple polygons. In this paper we follow the first line...
متن کاملWireless Localization within Orthogonal Polyhedra
In the wireless localization problem, given a polygon P ⊂ R, we have to place guards and fix their angular range such that P can be described using these guards. The guards describe P if for every point pair p ∈ P and q / ∈ P , there is a guard that sees p but does not see q. We consider the analogous problem in 3D: given a polyhedron P ⊂ R, place guards—which now are polyhedral cones—that coll...
متن کاملNon-orthogonal ray guarding
In an earlier paper the notion of a ray guard, a guard that can only see along a single ray, was introduced. Ray guarding means siting the fewest possible guards that guard all adjacencies (shared edges or parts of edges) in an orthogonal arrangement of adjacent nonoverlapping rectangles. In the earlier paper the problem was restricted by requiring that the direction of sight be parallel to one...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008