Securing Pathways with Orthogonal Robots

TL;DR

This paper presents a linear-time method for optimally guarding orthogonal pathways with the fewest robots, addressing a specific efficient solution within a complex NP-hard problem.

Contribution

It introduces a novel linear-time algorithm for minimizing orthogonal robots needed to secure pathways, focusing on orthogonal pathways with dual graph structures.

Findings

Minimum number of robots can be determined in linear time for pathways.

The general problem for polygons remains NP-hard.

Robots can be placed anywhere within the polygon.

Abstract

The protection of pathways holds immense significance across various domains, including urban planning, transportation, surveillance, and security. This article introduces a groundbreaking approach to safeguarding pathways by employing orthogonal robots. The study specifically addresses the challenge of efficiently guarding orthogonal areas with the minimum number of orthogonal robots. The primary focus is on orthogonal pathways, characterized by a path-like dual graph of vertical decomposition. It is demonstrated that determining the minimum number of orthogonal robots for pathways can be achieved in linear time. However, it is essential to note that the general problem of finding the minimum number of robots for simple polygons with general visibility, even in the orthogonal case, is known to be NP-hard. Emphasis is placed on the flexibility of placing robots anywhere within the polygon, whether on the boundary or in the interior.