Guarding the Vertices of an Orthogonal Terrain using Vertex Guards
Saeed Mehrabi
TL;DR
This paper presents an exact algorithm for optimally guarding convex vertices of orthogonal terrains using the fewest reflex vertices, addressing a specific geometric guarding problem.
Contribution
It introduces a novel exact algorithm for the vertex guarding problem on orthogonal terrains, focusing on convex and reflex vertices.
Findings
The algorithm guarantees minimal reflex vertices for guarding convex vertices.
It advances understanding of terrain guarding in orthogonal terrains.
Provides a computational method for optimal vertex guarding.
Abstract
A terrain T is an x-monotone polygonal chain in the plane; T is orthogonal if each edge of T is either horizontal or vertical. In this paper, we give an exact algorithm for the problem of guarding the convex vertices of an orthogonal terrain with the minimum number of reflex vertices.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Robotic Path Planning Algorithms · Complexity and Algorithms in Graphs