Minimum vertex guard problem for orthogonal polygons: a genetic approach

Authors:
Antonio L. Bajuelos;Santiago Canales;Gregorio Hernández;Ana Mafalda Martins
Affiliations:
Universidade de Aveiro, Departamento de Matematica & CEOC, Aveiro, Portugal;Universidad Pontificia Comillas de Madrid, Escuela Técnica Superior de Ingeniería, ICAI, Madrid, Spain;Universidad Politécnica de Madrid, Facultad de Informática, Madrid, Spain;Universidade de Aveiro, Departamento de Matematica & CEOC, Aveiro, Portugal
Venue:
MAMECTIS'08 Proceedings of the 10th WSEAS international conference on Mathematical methods, computational techniques and intelligent systems
Year:
2008

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Abstract

The problem of minimizing the number of guards placed on vertices needed to guard a given simple polygon (MINIMUM VERTEX GUARD problem) is NP-hard. This computational complexity opens two lines of in vestigation: the development of algorithms that determine approximate solutions and the determination of optimal solutions for special classes of simple polygons. In this paper we follow the first line of investigation proposing an approximation algorithm based on the general metaheuristic Genetic Algorithms to solve the MINIMUM VERTEX GUARD problem.