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All Journal dCartesian: Jurnal Matematika dan Aplikasi Jurnal MIPA
Benny Pinontoan
Jurusan Matematika, FMIPA, UNSRAT
Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Mathematics Physics

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Region Coloring in Minahasa Regency Using Sequential Color Algorithm Ingamita, Yevie; Nainggolan, Nelson; Pinontoan, Benny
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 8, No 2 (2019): September 2019
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (478.685 KB) | DOI: 10.35799/dc.8.2.2019.23956

Abstract

Graph Theory is one of the mathematical sciences whose application is very wide in human life. One of theory graph application is Map Coloring. This research discusses how to color the map of Minahasa Regency by using the minimum color that possible. The algorithm used to determine the minimum color in coloring the region of Minahasa Regency that is Sequential Color Algorithm. The Sequential Color Algorithm is an algorithm used in coloring a graph with k-color, where k is a positive integer. Based on the results of this research was found that the Sequential Color Algorithm can be used to color the map of Minahasa Regency with the minimum number of colors or chromatic number χ(G) obtained in the coloring of 25 sub-districts on the map of Minahasa Regency are 3 colors (χ(G) = 3).
Derivation of Quantum Guarded Command Language Program for Average Telap, Cherry; Pinontoan, Benny; Titaley, Jullia
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 4, No 2 (2015): September 2015
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (676.22 KB) | DOI: 10.35799/dc.4.2.2015.9055

Abstract

Has conducted research to determine the derivation of quantum guarded command language (qGCL) program for average. Initially calculation of average value was made in guaded command language (GCL) which is then implemented on a digital computer into the Pascal programming language. Furthermore GCL to calculate the average value was analyzed again to be made in the quantum guarded command language (qGCL). qGCL implementation is on a quantum computer is a future computer could perform calculations very quickly because it uses a superposition state is referred to as quantum bits (qubits). Keywords : GCL, qGCL, Quantum Computer
Data Compression Using Shannon-Fano Algorithm Lamorahan, Christine; Pinontoan, Benny; Nainggolan, Nelson
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 2, No 2 (2013): September, 2013
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (338.775 KB) | DOI: 10.35799/dc.2.2.2013.3207

Abstract

Abstract Communication systems in the world of technology, information and communication are known as data transfer system. Sometimes the information received lost its authenticity, because size of data to be transferred exceeds the capacity of the media used. This problem can be reduced by applying compression process to shrink the size of the data to obtain a smaller size. This study considers compression for data text using Shannon – Fano algorithm and shows how effective these algorithms in compressing it when compared with the Huffman algorithm. This research shows that text data compression using Shannon-Fano algorithm has a same effectiveness with Huffman algorithm when all character in string all repeated and when the statement short and just one character in the statement that repeated, but the Shannon-Fano algorithm more effective then Huffman algorithm when the data has a long statement and data text have more combination character in statement or in string/ word. Keywords: Data compression, Huffman algorithm, Shannon-Fano algorithm Abstrak Sistem komunikasi dalam dunia teknologi informasi dan komunikasi dikenal sebagai sistem transfer data. Informasi yang diterima kadang tidak sesuai dengan aslinya, dan salah satu penyebabnya adalah besarnya ukuran data yang akan ditransfer melebihi kapasitas media yang digunakan. Masalah ini dapat diatasi dengan menerapkan proses kompresi untuk mengecilkan ukuran data yang besar sehingga diperoleh ukuran yang lebih kecil. Penelitian ini menunjukan salah satu kompresi untuk data teks dengan menggunakan algoritma Shannon – Fano serta menunjukan seberapa efektif algoritma tersebut dalam mengkompresi data jika dibandingkan dengan algoritma Huffman. Kompresi untuk data teks dengan algoritma Shannon-Fano menghasilkan suatu data dengan ukuran yang lebih kecil dari data sebelumnya dan perbandingan dengan algoritma Huffman menunjukkan bahwa algoritma Shannon- Fano memiliki keefektifan yang sama dengan algoritma Huffman jika semua karakter yang ada di data berulang dan jika dalam satu kalimat hanya ada satu karakter yang berulang, tapi algoritma Shannon-Fano lebih efektif jika kalimat lebih panjang dan jumlah karakter di dalam kalimat atau kata lebih banyak dan beragam. Kata kunci: Algoritma Huffman, Algoritma Shannon-Fano, Kompresi data
Application of Decision Support System Based On GUI to Determine The Best Mall In Manado City By Using ELECTRE Method Binowo, Kenedi; Rindengan, Altien Jonathan; Pinontoan, Benny
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 7, No 1 (2018): Maret 2018
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (626.671 KB) | DOI: 10.35799/dc.7.1.2018.19550

Abstract

Mall is a shopping center that has numerous functions, and the mall has become a place of human survival, therefore this research is done to choose the best mall in Manado city which is Jumbo, Mega Trade Center, Manado Town Square, Mega Mall, and Multimart. The ELECTRE method is one of the multi-criteria decision-making methods based on the concept of outranking by using pairwise comparisons of alternatives based on each appropriate criterion.  The purpose of this research is to find out the best mall in Manado city based on ELECTRE method, and to find out the most important thing in designing GUI based application system. GUI is a decision support program in mathematics programs. From the research result using ELECTRE method can be known that the best mall in Manado city is Mega Mall, because from the best calculation result is (Alternative 4), where if indicates that alternative is the chosen alternative. The results of GUI-based applications it has been perform a result that the most important thing in the making is: There must be a place of input value, there should be an output display, and there should be execution buttons, and most importantly also that must create a coding in accordance with the programming language that can be read by mathematics programs.K e y w o r d s:  Mall, ELECTRE Method, Decision Support System, GUI Application
Quantum Guarded-Command Language (qGCL) for Maximum Value Putri, Aisya; Titaley, Jullia; Pinontoan, Benny
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 6, No 1 (2017): Maret 2017
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (794.517 KB) | DOI: 10.35799/dc.6.1.2017.14988

Abstract

On a classical computer or a binary computer, calculations are done simultaneously so as to produce the equations and algorithms. The result of this research shows that to determined maximum value specified in the algorithm using quantum Guarded-Command Language (qGCl) in quantum computer. Initially determine of maximum value was construct in Djikstra’s Guarded-Command Language (GCL) which is then implemented on Zuliani’s probability Guarded-Command Language (pGCL) furthermore applying to quantum Guarded-Command Language (qGCL) for last result. Of concern here is the speed in resolving a problem or calculate problem. Due to the Quantum Computer has a Quantum Bit (qubit) and a phenomenon commonly called superposition. Keywords: GCL, pGCL, qGCL, quantum computer.
The Implementation of Bipartite Graph To Minimize Crossing Number Problem of Crossroads in Manado Nazareth, Timboeleng Axellica; Montolalu, Chriestie E.J.C; Pinontoan, Benny
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 8, No 2 (2019): September 2019
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (590.022 KB) | DOI: 10.35799/dc.8.2.2019.24240

Abstract

The Implementation Of Bipartite Graph To Minimize Crossing Number Problem Of  Crossroads In Manado. Supervised by BENNY PINONTAN as main supervisor and CHRIESTIE E. J. C. MONTOLALU as co-supervisor. In general, the crossroads are the meeting points of two-way roads from four different places. This causes cross direction at that point. There are various methods that can be used to minimize the crossing number problem crossroad, for example graph theory. The ability of graph theory can later help describe crossroads in Manado into graph, with nodes and lines. In this case, the crossing number problems will solve by bipartite graph. Bipartite graph is a graph that does not have an odd cycle, and can be partitioned into two parts of a set of vertices. Based on results of this research, the appropriate form of the bipartite graph is and  in two different form. First, with an isolated vertex, and second, without isolated vertex. In the case of crossroads, Bipartite graph turns out to be one method that is very suitable and helps determine the crossing number and its solution quickly.
Rectilinear Monotone r-Regular Planar Graphs for r = {3, 4, 5} Wulur, Arthur; Pinontoan, Benny; Mananohas, Mans
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 4, No 1 (2015): Maret 2015
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (731.825 KB) | DOI: 10.35799/dc.4.1.2015.8318

Abstract

A graph G consists of non-empty set of vertex/vertices (also called node/nodes) and the set of lines connecting two vertices called edge/edges. The vertex set of a graph G is denoted by V(G) and the edge set is denoted by E(G). A Rectilinear Monotone r-Regular Planar Graph is a simple connected graph that consists of vertices with same degree and horizontal or diagonal straight edges without vertical edges and edges crossing. This research shows that there are infinite family of rectilinear monotone r-regular planar graphs for r = 3and r = 4. For r = 5, there are two drawings of rectilinear monotone r-regular planar graphs with 12 vertices and 16 vertices. Keywords: Monotone Drawings, Planar Graphs, Rectilinear Graphs, Regular Graphs
Application Of Vehicle Routing Problem Using Clarke And Wright Algorithm For Distribution Of White Sugar By “Toko Bersama Trader” Morihito, Rondo; Montolalu, Chriestie; Pinontoan, Benny
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 7, No 2 (2018): September 2018
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (731.169 KB) | DOI: 10.35799/dc.7.2.2018.20627

Abstract

The problem which is often experienced in the delivery of goods from distributor to the destination is the delivery route which is not sufficient with the capacity of the vehicle. This matter is very important because it can affect the trust of the clients on the shippers in the distributor. This problem can be analyzed using Capacitated Vehicle Routing Problem (CVRP) with Clarke and Wright Algorithm. This research begins with determining the distance between all coordinates with Euclidean Distance, making the distance matrix between places to go. After that, the calculation CVRP using Clarke and Wright Algorithm is exected in this study, a calculate CVRP using Clarke and Wright algorithm can help of the computer. The study was conducted at 15 shop coordinates, the results obtained by 4 routes with total load 3750 kg and distance 29.8510 km. Route of delivery the first route 1100 kg load and distance 11.5963 km, second route 1000 kg load and distance 6.6493 km, third route 1000 kg load and distance 2.7549 km, and the fourth route 650 kg load and distance 8.8505 km.Keywords:  Distributor, Vehicle Routing Problem, Capacitated Vehicle Routing Problem, Clarke and Wright Algorithm
Construction of Error-Correction Code Application by Applying Finite Field and Hadamard Matrix Theory Pongoh, Robinson; Pinontoan, Benny; Weku, Winsy
Jurnal MIPA Vol 1, No 1 (2012)
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/jm.1.1.2012.430

Abstract

Dalam dunia elektronik dan digital, informasi dapat dengan mudahditransfer melalui saluran komunikasi. Pada data yang ditransfer galatdapat muncul dikarenakan oleh berbagai akibat. Untuk menghindarimasalah ini diperlukan kode perbaikan-galat bersama aplikasinya. Konsepdari kode perbaikan-galat adalah untuk menambahkan bit-tambahanpada data agar disaat pengiriman, data tersebut lebih kuat dalammenghadapi gangguan yang hadir di saluran komunikasi. Random ParityCode (RPC) yang dikemukakan oleh Hershey dan Tiemann (1996) adalahsalah satu dari kode yang dimaksud. Artikel ini menunjukan pembuatanaplikasi kode perbaikan-galat yang dibuat berdasarkan konsep RPCdengan bantuan teori Lapangan Terbatas dan Matriks Hadamard. Aplikasidibuat menggunakan Metode Rapid Application Development (RAD).Aplikasi dihasilkan dalam bentuk perangkat lunak komputer. Perangkatlunak tersebut menjadi lebih efisien dengan menerapkan konsepalgoritma “Divide and Conquer”.
Book Embedding of Infinite Family ((2h+3 2))-Crossing-Critical Graphs for h=1 with Rational Average Degree r∈(3.5,4) Wilar, Sheren H.; Pinontoan, Benny; Montolalu, Chriestie E.J.C.
d'CARTESIAN:Jurnal Matematika dan Aplikasi Vol 9, No 2 (2020): September 2020
Publisher : Universitas Sam Ratulangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (562.698 KB) | DOI: 10.35799/dc.9.2.2020.29166

Abstract

A principal tool used in construction of crossing-critical graphs are tiles. In the tile concept, tiles can be arranged by gluing one tile to another in a linear or circular fashion. The series of tiles with circular fashion form an infinite graph family. In this way, the intersection number of this family of graphs can be determined. In this research, has been formed an infinite family graphs Q_((1,s,b) ) (n) with average degree r between 3.5 and 4. The graph formed by gluing together many copies of the tile P_((1,s,b) ) in circular fashion, where the tile P_((1,s,b) ) consist of two identical pieces of tile. And then, the graph embedded into the book to determine the pagenumber that can be formed. When embed graph into book, the vertices are put on a line called the spine and the edges are put on half-planes called the pages. The results obtained show that the graph Q_((1,s,b) ) (n) has 10-crossing-critical and book embedding of graph has 4-page book.
Co-Authors Arthur Wulur, Arthur Binowo, Kenedi Cherry Telap, Cherry Chriestie E.J.C. Montolalu, Chriestie E.J.C. Chriestie Montolalu, Chriestie Christine Lamorahan Chungdinata, Stephanie E Ingamita, Yevie Jullia Titaley Juwita Rawung Luther Latumakulita Makalew, Roy A.M Mans Mananohas, Mans Montolalu, Chriestie E.J.C Morihito, Rondo Morihito, Rondo V.S.A Nazareth, Timboeleng A Nazareth, Timboeleng Axellica NELSON NAINGGOLAN Pulukadang, M Iqbal Putri, Aisya Rindengan, Altien Jonathan Robinson Pongoh Sumual, Gery Josua Wilar, Sheren H. Winsy Weku