Optimizing Modem Placement in UPI Building FPMIPA using the Illumination Model
Abstract
Since a reliable internet signal has become an essential and significant need nowadays, the existence of modems as transmitters of internet signals is also crucial; modems transmit the internet signal (without cable), which is then captured by devices. This research aims to construct a mathematical model to determine the minimum number of modems and their placement so that the entire building FPMIPA-A of UPI has a good internet signal. In this research, we assume that the modem can pass through at most two walls, and the area studied is limited to the first floor of FPMIPA-A. The model is based on the illumination problems theorems, one of which states that every monotone 6-gon can be covered by a single 2-modem point placed at one of its two leftmost (or rightmost) vertices. By the theorem, we view the layout of the rooms in the building as a combination of polygons. The results show that 12 modems are required to cover all areas on the first floor of FPMIPA-A to get a good signal.
Keywords: illumination problem; modem; polygonal regions; optimal modem placement; building FPMIPA A.
Abstrak
Saat ini, kebutuhan akan sinyal internet yang andal menjadi kebutuhan penting dan utama. Modem sebagai pemancar sinyal internet mengirimkan sinyal internet (tanpa kabel) dan kemudian ditangkap oleh perangkat. Penelitian ini bertujuan untuk membangun model matematika yang menentukan jumlah minimum modem dan penempatannya agar seluruh gedung FPMIPA-A UPI mempunyai sinyal internet yang baik. Pada penelitian ini diasumsikan modem dapat menembus paling banyak dua dinding dan area yang diteliti dibatasi pada lantai 1 gedung FPMIPA-A UPI. Model matematika untuk masalah penempatan modem ini didasarkan pada teorema masalah iluminasi, yang salah satunya menyatakan bahwa setiap 6-gon monoton dapat ditutupi oleh satu titik 2-modem yang ditempatkan di salah satu dari dua simpul paling kiri (atau paling kanan). Berdasarkan teorema tersebut, tata ruang pada lantai 1 gedung FPMIPA-A UPI dipandang sebagai kombinasi poligon. Hasil penelitian menunjukkan bahwa dibutuhkan 12 modem untuk mencakup seluruh area di lantai 1 FPMIPA-A guna mendapatkan sinyal yang baik.
Kata Kunci: masalah iluminasi; modem, daerah poligon; penempatan modem secara optimal; gedung FPMIPA A.
2020MSC: 90C90.
Keywords
References
O. Aichlozer, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, J. Urrutia, and B. Vogtenhuber, "Modem illumination of monotone polygon," Computational Geometry, vol. 68, pp. 101-118, 2018.
V. Chvátal, "A combinatorial theorem in plane geometry," Journal of Combinatorial Theory, Series B, vol.18, no.1, pp. 39-41, 1975.
M. Abrahamsen, A. Adamaszek, and T. Miltzow, "The art gallery problem is ∃ ℝ-complete," ACM Journal of the ACM (JACM), vol. 69, no.1, pp. 1-70, 2021.
J. Urrutia, Art gallery and illumination problems, Handbook of computational geometry, pp. 973-1027, North-Holland, 2000
M. Ernestus, S. Friedrichs, M. Hemmer, J. Kokemüller, A. Kröller, M. Moeini, & C. Schmidt, “Algorithms for art gallery illumination,” Journal of Global Optimization, vol. 68, pp. 23-45, 2017.
S. K. Ghosh, “Approximation algorithms for art gallery problems in polygons,” Discrete Applied Mathematics, vol. 158, no. 6, pp. 718-722, 2010.
E. I. G. Handayani, K. Yulianti, and K. Novianingsih, “Art Gallery Problem untuk 1-Guarded Guards Dan 2-Guarded Guards pada Poligon Orthogonal,” Jurnal EurekaMatika, vol 8, no. 1, pp. 15-25, 2020.
R. Fabila-Monroy, A. R. Vargas, and J. Urrutia, On modem illumination problems, XIII encuentros de geometria computacional, Zaragoza: Prensas de la Universidad de Zaragoza, 2009.
F. Duque, and C. Hidalgo-Toscano, “An upper bound on the k-modem illumination problem,” International Journal of Computational Geometry & Applications, vol. 25, no.04, pp. 299-308, 2015.
M. S. Shamaee, A. M. Khorasani, and M. Eskandari, “The Illumination of Polygonal Regions with Modems,” The CSI Journal on Computer Science and Engineering, vol.8 no.2, pp. 21-28, 2010.
B. Ballinger, et al, Coverage with k-transmitters in the presence of obstacles, in: W. Wu, O. Daescu (Eds.) Comb. Opt. and Appl., in: Lecture Notes in Computer Science, vol. 6509, pp. 1-15, Berlin: Springer-Heidelberg, 2010.
S. Cannon, T. G. Fai, J. Iwerks, U. Leopold, and C. Schmidt, "Combinatorics and complexity of guarding polygons with edge and point 2-transmitters,” Computational Geometry, vol. 68, pp. 89-100, 2018.
S. S. Mahdavi, S. Seddighin, and M. Ghodsi, “Covering orthogonal polygons with sliding k-transmitters,” Theoretical Computer Science, vol. 815, pp. 163-181, 2020.
S. M. H. Mousavi, V. Charles, and T. Gherman, "An evolutionary support vector finder method," Expert Systems with Applications, vol. 150, no. 1-2, pp. 171-184, 2020.
DOI: 10.15408/inprime.v6i2.41452
Refbacks
- There are currently no refbacks.
.
