Prim's Algorithm for Optimizing Fiber Optic Trajectory Planning

IJSRST1736117 | Received : 15 August 2017 | Accepted : 29 August 2017 | July-August-2017 [(3) 6: 504-509]
© 2017 IJSRST | Volume 3 | Issue 6 | Print ISSN: 2395-6011 | Online ISSN: 2395-602X
Themed Section: Science and Technology
504
Prim's Algorithm for Optimizing Fiber Optic Trajectory Planning
Muhammad Iqbal1
, Andysah Putera Utama Siahaan2
, Nathania Elizabeth Purba3
, Dedi Purwanto4
1,2,4
Faculty of Computer Science, Universitas Pembangnuan Panca Budi, Medan, Indonesia
3
Faculty of Computer Science and Information Technology, Universitas Sumatera Utara, Medan, Indonesia
2
Ph.D. Student of School of Computer and Communication Engineering, Universiti Malyasia Perlis, Kangar, Malaysia
ABSTRACT
The transition of copper cable technology to fiber optic is very triggering the development of technology where data
can be transmitted quickly and accurately. This cable change can be seen everywhere. This cable is an expensive
cable. If it is not installed optimally, it will cost enormously. This excess cost can be used to other things to support
performance rather than for excess cable that should be minimized. Determining how much cable use at the time of
installation is difficult if done manually. Prim's algorithm can optimize by calculating the minimum spanning tree
on branches used for fiber optic cable installation. This algorithm can be used to shorten the time to a destination by
making all the points interconnected according to the points listed. Use of this method helps save the cost of fiber
optic construction.
Keywords : Fiber Optic, Prim’s Algorithm, Shortest Path
I. INTRODUCTION
Fiber Optic is a thing that has become the current
technology needs, especially now where the needs of
communication and technology are getting higher. It is
used primarily for the internet in all places, at home, at
the office or in public areas. Substitution of old channels
is rampant everywhere. Copper wires are still an
inexpensive option to transmit data in all directions.
However, with the growing amount of data, transmission
delivery requires a fast time so that the data does not
experience delays. It occurs when streaming video using
the internet. Videos that have an excellent quality will
experience a dashed transmission.
The fastest data transmission at a previous time was to
utilize electrical signals with copper wires. Then came
the wireless technology with GSM signal which
currently supports 4G technology. Fiber optic appears
and is in high demand because its speed is much faster
than the speed of electricity or sound. The transmission
uses light at speeds of 300,000,000 meters per second
while the sound speed is only 343 meters per second.
Based on this speed, the fiber optic solution is used as
the data carrier in the next era. However, in the
construction of this network, many obstacles faced,
especially in the field of costs incurred. This cable is
very expensive, and if not calculated carefully, it will
harm some parties including harming the state if the
project is controlled by the state. This cabling requires a
good algorithm to optimize cable requirements. The
shortest route search is an action to reduce cost [5].
Prim's algorithm is one algorithm that can be used to
calculate minimum cable usage to minimize cost. This
algorithm will look for shorter connections between the
two branching points of the cable. This use is expected
to reduce the number of cables used on each transmitter
pole.
II. METHODS AND MATERIAL
2.1 Fiber Optic
Fiber optic is a medium of information that is now used
to connect computer networks. This transmission device
is made of glass fiber and plastic that uses light bias in
the process of sending information. The light source
used is a laser. Laser becomes an option because it has a
very narrow spectrum. The use of fiber optic cables is
based on the speed at which data transmission. The
emitted signal is not affected by electromagnetic waves
as in copper wires. The induction will occur in copper
cables when there are cables adjacent to other cables

International Journal of Scientific Research in Science and Technology (www.ijsrst.com) 505
including the influence of radio frequency waves of
communication. Fiber optic is used as the backbone of a
network. It is an unstable wireless transmission if there
is a radio frequency colliding [8].
Fiber optic has two modes, single and multi mode.
• Single-mode fibers have a small core that is
0.00035-inch diameter or 9 microns and serves to
transmit infrared laser light. The wavelength
approximately 1300-1550 nanometers.
• Multi-mode fibers have a larger core that is 0.0025-
inch diameter or 62.5 microns and serves to transmit
infrared laser light with a wavelength of about 850-
1300 nanometers.
The single mode has a small core size, laser light source,
unlimited bandwidth, and long distances. The multi
mode has a larger core size, the source of the laser beam,
the limited bandwidth, the distance of the beam is not so
far away. The basic structure of fiber optic consists of
three parts: core, cladding, and buffer/coating. Core and
cladding are made of glass while the buffer is made of
plastic to maintain flexibility.
Fusion Splicer is a tool for connecting glass-based
optical fibers that implement an electric power that has
been converted into a laser beam-shaped light media that
serves to heat the broken glass on the core so that it
reconnects properly. It must have high accuracy so that
the cable at the time of splicing can be near perfect [9].
The process of sending information on fiber optic cable
is by applying the welding of glass media, and there is a
glass melting process that produces the connection
without any gaps. This connection may fail if the cable
connection does not follow the procedure properly. The
connection process should be repeated in case of error. It
aims to create damping below 0.25 dB. Improper
connection process will result in high Bit Error Rate. It
results in high resistance and makes the transmission
flow to the device will not run perfectly.
2.2 Prim’s Algorithm
The minimum range tree is a way to form a link to the
graph to all points with the smallest weights until the
minimum distance is obtained [1][4][10].Prim's
algorithm was discovered in 1930 by a mathematician
named Vojtěch Jarník. Robert C. Prim and Dijkstra re-
examined this algorithm separately in 1957 and 1959.
Prim's algorithm is a method in graph theory to find the
minimum spanning tree for an interconnected weighted
graph [2][3]. It means that a subset of edges that form a
tree containing nodes. It aims to minimize the overall
weighting of all edges in the graph. If the graph is not
connected, the graph has only one minimum range tree
for one of the connected components [6][7].
Table 1. Initial weight
Source Dest. Weight
A B 4
F 5
B A 4
C 5
E 4
F 2
C B 5
D 6
E 2
F 3
D C 6
E 3
E B 4
C 2
D 3
F 10
F A 5
B 2
C 3
E 10
Figure 1. Initial weighted graph

Table 1 and Figure 1 are preliminary data for
weighted graphs. Six nodes are forming the graph, and
some of the nodes are interconnected [11]. Be aware this
node will get the shortest path to connect the nodes.
Figure 2. Step one
Figure 3. Step two
Figure 4. Step three
Figure 5. Step four
Figure 6. Step five
The node search starts from A to F, so all nodes are
connected. The use of Prim's algorithm works if there
are nodes that have multiple branches. Otherwise, no
algorithm needs to be applied. Figure 2 to 6 describes
the process of determining which nodes will be the
minimum spanning tree. The nodes that have the
smallest weights will always be selected to be the next
route. So the results obtained are A-B-F-C-E-D as in
Figure 6.
III. RESULTS AND DISCUSSION
This test is trying to apply the optical fiber cable
withdrawal in a particular area. There are 24 points to be
linked directly. Some of the points are interconnected, so
it should be determined which point further shortens the
time and length. Table 2 describes the location of the
coordinate points as examples of their application.
Figure 7. Fiber optic graph route

Table 2. Fiber optic coordinate
No. X Y Branches
0 22 29 1, 7
1 39 34 0, 2, 3
2 50 58 1, 3, 7, 8, 23
3 63 20 1, 2, 5
4 77 53 5, 6, 9, 23
5 83 26 4, 6, 21
6 96 45 4, 5, 9, 21
7 20 56 0, 2, 8
8 47 78 2, 7, 9, 11, 23
9 80 76 4, 6, 8, 10, 11, 23
10 115 96 9, 11, 12, 13
11 37 124 8, 9, 10
12 145 138 10, 13, 18
13 157 117 10, 14, 18
14 157 72 13, 15, 19
15 190 77 14, 16, 17, 18
16 210 80 15, 17, 18
17 177 21 15, 16, 19
18 207 121 12, 13, 15, 16
19 142 20 14, 17, 20, 22
20 128 13 19, 21, 22
21 100 20 5, 6, 20, 22
22 121 23 19, 21
23 67 61 2, 4, 8, 9
Figure 7 is a graph formed based on the coordinates
shown in Table 8. Each node will be connected directly
to its branches. Each node intersection has weights that
are calculated based on Euclidean Distance. For example,
the weights from node 0 to 1 can be seen in the
following calculations:
D(0, 1) = √(𝑥1 − 𝑥0)2 + (𝑦1 − 𝑦0)2
= √(39 − 22)2 + (34 − 29)2
= √172 + 52
= √289 + 25
= √314
= 17.7200451466693
Table 3. Weight result
Node 1 Node 2 Weight
[0] [1] 17,72
[0] [7] 27,07
[1] [0] 17,72
[1] [2] 26,4
[1] [3] 27,78
[2] [1] 26,4
[2] [3] 40,16
[2] [7] 30,07
[2] [8] 20,22
[2] [23] 17,26
[3] [1] 27,78
[3] [2] 40,16
[3] [5] 20,88
[4] [5] 27,66
[4] [6] 20,62
[4] [9] 23,19
[4] [23] 12,81
[5] [4] 27,66
[5] [6] 23,02
[5] [21] 18,03
[6] [4] 20,62
[6] [5] 23,02
[6] [9] 34,89
[6] [21] 25,32
[7] [0] 27,07
[7] [2] 30,07
[7] [8] 34,83
[8] [2] 20,22
[8] [7] 34,83
[8] [9] 33,06
[8] [11] 47,07
[8] [23] 26,25

[9] [4] 23,19
[9] [6] 34,89
[9] [8] 33,06
[9] [10] 40,31
[9] [11] 64,44
[9] [23] 19,85
[10] [9] 40,31
[10] [11] 82,87
[10] [12] 51,61
[10] [13] 46,96
[11] [8] 47,07
[11] [9] 64,44
[11] [10] 82,87
[12] [10] 51,61
[12] [13] 24,19
[12] [18] 64,29
[13] [10] 46,96
[13] [14] 45
[13] [18] 50,16
[14] [13] 45
[14] [15] 33,38
[14] [19] 54,12
[15] [14] 33,38
[15] [16] 20,22
[15] [17] 57,49
[15] [18] 47,17
[16] [15] 20,22
[16] [17] 67,6
[16] [18] 41,11
[17] [15] 57,49
[17] [16] 67,6
[17] [19] 35,01
[18] [12] 64,29
[18] [13] 50,16
[18] [15] 47,17
[18] [16] 41,11
[19] [14] 54,12
[19] [17] 35,01
[19] [20] 15,65
[19] [22] 21,21
[20] [19] 15,65
[20] [21] 28,86
[20] [22] 12,21
[21] [5] 18,03
[21] [6] 25,32
[21] [20] 28,86
[21] [22] 21,21
[22] [19] 21,21
[22] [21] 21,21
[23] [2] 17,26
[23] [4] 12,81
[23] [8] 26,25
[23] [9] 19,85
Table 3 shows the weighting results based on the
previously defined coordinates. After the weights are
obtained, the Prim's algorithm process can be
implemented. The minimum spanning tree results are as
in Figure 8. If there are branches, then the weights are
selected based on the smallest weights. The Greedy
algorithm inspires it.
Figure 8. Prim’s algorithm result

IV. CONCLUSION
Prim's algorithm performs searches on notes that have
the shortest weights. This process can be done on fiber
optic cabling. Due to very high cable prices, this
algorithm has an important role to play in reducing
construction costs. It always produces sides that are
members of the minimum spanning tree. It makes every
step of the search efficient and effective. However, in a
graph that has many circuits, this algorithm takes a long
time to check the existence of the circuit against the
spanning tree that has been formed. In many branch
graphs such as complete graphs, this method becomes an
obstacle in the problem of graduation. This algorithm is
considered good enough to be applied to the
development of fiber optic lines so that the cost is not a
waste.
V. REFERENCES
[1]. N. P. Akpan and I. A. Iwok, "A Minimum
Spanning Tree Approach of Solving a
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[2]. S. Dagar, "Modified Prim's Algorithm,"
International Journal of Computer and Information
Technology, vol. 3, no. 2, pp. 26-29, 2012.
[3]. T. O. Arogundade, B. Sobowale and T. A.
Akinwale, "Prim Algorithm Approach to
Improving Local Access Network in Rural Areas,"
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Engineering, vol. 3, no. 3, pp. 413-417, 2011.
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Technique to Construct a Minimum Spanning
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[5]. A. P. U. Siahaan, "Heuristic Function Influence to
the Global Optimum Value in Shortest Path
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[7]. W.-C. Chang, T.-H. Wang and Y.-D. Chiu, "Board
Game Supporting Learning Prim’s Algorithm and
Dijkstra’s Algorithm," International Journal of
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[8]. A. Amaku, R. E. Watti and J. Joshua, "Optic Fiber
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[11]. Ray, "Algoritma Prim," 20 April 2011. [Online].
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