(untitled) (Jurnal EurekaMatika, 2020)
The Art Gallery Problem for k-guarded guards is the problem of determining the minimum number of guards who can each see k other guards (k-guarded guards) and can monitor all parts of a polygon with n vertices. The placement of k-guarded guards is necessary to enhance the security of a room against theft, not only from external visitors but also from the guards themselves. This research discusses the art gallery problem for k-guarded guards on orthogonal polygons for k=1 and k=2. For k=1, known as the Art Gallery Problem for 1-guarded guards, the problem has been solved through the concept of graph coloring. In this study, a new theorem is constructed using the same concept as a solution for k=2. Furthermore, the placement of 1-guarded guards is implemented in a department store in the city of Bandung. Keywords: Art gallery problem for 2-guarded guards, Art gallery problem for guarded guards, Graph coloring, Orthogonal polygon ABSTRAK Art Gallery Problem for k-guarded guards adalah masalah penentuan jumlah minimal penjaga yang dapat melihat k penjaga lainnya (k-guarded guards) dan dapat mengawasi seluruh bagian poligon dengan simpul. Penempatan k-guarded guards diperlukan untuk meningkatkan pengawasan suatu ruangan dari pencurian yang bukan hanya berasal dari pengunjung luar, tetapi juga dari penjaga. Penelitian ini membahas art gallery problem for k-guarded guards pada poligon orthogonal untuk dan . Untuk yang dikenal dengan art gallery problem for 1-guarded guards, masalah telah diselesaikan melalui konsep pewarnaan graf. Pada penelitian ini dikontruksi teorema baru melalui konsep yang sama sebagai penyelesaian untuk . Selanjutnya, penempatan 1-guarded guards diimplementasikan pada suatu toserba di kota Bandung.