Shortest Path Problem Solving in the Installation of DataInternet Network Using Apriori Algorithm

Shortest-Path Problem Solving in the Installation of
Data/Internet Network Using Apriori Algorithm
Ali Akbar 1

Nurul Adhayanti2

Faculty of Industrial Technology
Gunadarma University
Indonesia
akbarjawas@gmail.com

Faculty of Computer Science
Gunadarma University
Indonesia
nuruladhayanti@gmail.com

Hendri Dwi Putra 4
Ike Putri Kusumawijaya

3

Faculty of Computer Science
Gunadarma University
Indonesia
Hendri_dpg@gmail.com

Faculty of Industrial Technology
Gunadarma University
Indonesia
ikeputri30@gmail.com

Abstract—Data network is something highly important in
information development. The commonly occuring problem is
how to connect every node or town to make it connected to the
network. We develop a softaware tool for solving shortestpath problem with Apriori algorithm to solve problem in the
shortest-path in the implementation of internet network. Based
on the research results by comparing Apriori Algorithm to
genetics, it is found that Apriori Algorithm has advantages
from the distance side used. In this case, for an experiment of
10 urban points, a distance of 38 for genetic algorithm is
found as compared to 29 using the apriori algorithm and the

value increases when 200 points are experimented, resulting in
a value of 5931 for genetic and 242.5 (for apriori). From this
result, it can then be concluded that apriori algorithm has the
advantage in the form of lesser distance than the genetic
algorithm hence it can be expected to reduce the costs.
Keywords—Apriori algorithm; Data network ; routing

I.

INTRODUCTION

This routing problem can be presented as how to determine
the shortest track to find a path between two nodes in such a
way that the total weight of its constituent arcs can be as
minimum as possible [1]. The shortest-path problems include
djikstra algorithm, Floyd-Warshall algorithm and BellmanFord algorithm. Meanwhile, according to Rama M Sukaton in
his research entitled “Penggunaan Algoritma Genetika Dalam
Jalur Terpendek Pada Jaringan Data”, the most appropriate
method for shortest-path problem with increasingly greater
and more complex number of nodes and tracks is genetic

algorithm, since despite the great number of tracks it can still
be solved and it moves towards an optimal point when it is
followed by increased size of other populations/paths [2]. In
this writing, we try to use apriori algorithm to solve shortestpath problem and try to compare it to genetic algorithm.

II.

EASE OF USE (LANDASAN TEORI )

A. Routing
A process of finding a path when there is a node in a
communication path in computer network is an important task
of a router device in a routing operation which is governed in
a protocol. There are two types of routing, i.e. static and
dynamic. In case of static routing, the path between nodes is
determined manually based on certain factors and saved in a
routing table [1]. For example, in Rama M Sukaton’s research
[2] it is shown router A which has two Ethernet interfaces and
one ISDN (Integrated Services Digital Network) interface,
where the Ethernet0 (e0) interface is assigned an IP address

10.1.1/24 and the Ethernet1 (e1) interface is assigned an IP
address 10.1.2.1/24.
B. Apriori algorithm
Apriori algorithm is a highly popular pattern-finding
algorithm in data mining technique. This algorithm is aimed at
finding an itemset combination which has a certain value of
frequency according to the desired criteria or filter. This
algorithm is proposed by R. Agrawal and R. Srikant. The
result of apriori algorithm can be used to help the management
make decisions. Apriori algorithm do an iterative approach
known as level-wise search, where k-itemset is used to explore
or find (k+1)-itemset. Therefore, apriori algorithm is divided
into several stages called iteration. Every iteration produces a
high-frequency pattern (frequent itemset) [3]. The theoretical
and empirical comparison of R-Apriori with existing apriori
implementation on the Spark platform (YAFIM) is done to
give insight into the superiority of our approach. In addition,
R-Apriori is more superior than classic Apriori on the Spark
for different standard dataset.[5]. In his research, Sayeth
Saabith concludes that Hadoop-MapReduce platform is

efficient and for the calculation of huge data the Hadoop-

Mapreduce which uses apriori algorithm is more efficient than
the data search on Hadoop-MapReduce platform with no
apriori algorithm.[6] From this, we can conclude that apriori
algorithm can increase the efficiency of data calculation
analysis. Additionally, another study mentions that aprioribased algorithm has better speed in managing greater data [7].
Apriori Algorithm Analysis with Router Shortest-Path
Problem

•

Apriori algorithm belongs to association rule mining, i.e. a
data mining technique to find the associative rule between
item combinations. An example of associative rule of routing
path analysis is to find out the shortest path in a large data
network. Using this knowledge, the router can regulate the
placement of paths with combination of several existing paths.
In determining an association rule, there is an
interestingness measure which is obtained from processing the

data using certain calculation. There are generally two
measures, namely [4]
•

•

Support (supporting value): a measure which shows
how large an item/itemset’s domination level is over
the entire data path. This measure decides whether an
item/itemset’s (data path) confidence is worth-finding
(for example, out of the entire existing networks, how
large is the domination level which shows that the
network is used.
Confidence (certainty/confidence value): a measure
which shows the relationship between 2 paths
conditionally (for example, how frequent is path B
used if the network is in use).

These two measures would eventually be useful in
determining the interesting association rules, i.e. to be

compared to a threshold determined by users. This threshold
generally consists of min_support and min_confidence, where
it is taken using the following ways [4]:
•

Finding all frequent itemsets, i.e. the itemsets with
support ≥ minimum support values which is the
threshold given by users. Where these itemset are a set
of items that is the combined purchased products.

•

Finding the association rule which is the confidence of
the obtained frequent itemset.

•

Finally, finding the rules which match the obtained
target users of the previous association rule mining
process. The obtained rules decribe the itemset

combination based on which the conclusion is drawn.

C. Genetic Algorithm
Genetic algorithm is an algorithm of search which depicts
biological evolution as a problem solving technique. Genetic
algorithm uses heuristic adaptive search technique which finds
a set of best solutions of the newly-produced/developing
population from the chromosome using an operator such as
selection, crossover and mutation. The most suitable is to
move the chromosome to the next generation. Weaker
candidate have less chance to move to the next generation.
This process is repeated until the chromosome has the best

solution which match the given problem. In summary, the
average population fitness increases in each iteration, hence by
repeating the process for more iterations, a better result is
found. Genetic algorithm has been widely studied and
experimented in various engineering fields. Genetic algorithm
provides an alternative method to solve existing problems
which are hard to solve using traditional methods. Genetic

algorithm can be applied to non-linear programming such as
problem of a moving salesman, minimum spanning tree,
scheduling issues and many more.[1]
For genetic algorithm, the basis is as follows:
•
•
•
•
•
•
•
•
•
•

generation = 0;
population [generation] = initializing population
(population);
evaluating Population (population [generation]);
While isTermination Condition Met () == false do

Parents= choose Parents (population [generation]);
population [generation + 1] = crossover (parents);
population [generation + 1] = mutating (population
[generation + 1]);
evaluating Population (population [generation]);
generation ++;
End of circle;

The pseudo code begins with creating an initial population
of genetic algorithm. This population is then evaluated to find
the fitness value of individuals. Furthermore, a check is run to
decide whether the condition for genetic algorithm termination
has been met. If it has not, the genetic algorithm begins the
iteration and the population runs through the first cycle of
crossover and mutation before it is finally be re-evaluated.
From here, the crossover and mutation continue to be applied
until the termination condition is met, and the genetic
algorithm ends. This pseudo code shows the basic process [8].
In another study it is stated that the Genetic algorithm will be
used to optimize the set of items and find the optimal and

appropriate association rule.[9] And this algorithm is also used
to determine the shortest path in previous studies [2]. Studies
using genetic algorithm to solve the shortest-path problems
have been conducted by Gihan Nagib and Wahied G. Ali. The
research finds that genetic algorithm has similar result as
Dijkstra algorithm [10]
Based on the several studies which indicate that apriori
algorithm can improve the performance of huge data
management, we try to use apriori algorithm to solve the
problem of determining the shortest path. It is expected that
using apriori algorithm, significant influence in the selection
of shortest path can be obtained. As a comparison, we use
Genetic algorithm which has been previously used to solve the
shortest-path problem in data network.
III.

RESEARCH METHOD

3.1. Research Method
In this research we try to find out whether association rule
mining can be used in the shortest path and comparison with
genetic algorithm

In the apriori algorithm explained in this research, the type
of representation used is to use support and confidence, using
network nodes with positive numbers 1,2,3..,n where is the
amount of nodes in network, every amount of nodes serves as
input of support and confidence minimum values, thus it can
be depicted as a string of codes of nodes in network which
does not repeat and represents a sequence or path.
The research design flow method performed in apriori
algorithm to determine the shortest path in data
communication has the following flow:
•

Network traffic data, is a simulation of network points
which are likened to be in an area and town, which will
be used as an input of apriori algorithm

•

Apriori algorithm is done by turning the traffic data lalu
into input/network. In the initial process, the data will be
collected to be a database, then it will be processed to
generate a network with apriori iteration to obtain an
optimized shortest route of a network traffic data

•

Computation is the combination of results from the
traffic data with the design resulting from literature study

•

The resulting shortest path is the generated from the
computation containing description of the resulting
shortest path with optimized iteration from the achieved
shortest path

The implementation of apriori algorithm uses software
MATLAB R2013b.
The inputs from the program are:
• File input, containing network data such as number of
towns with random values,
• Apriori algorithm parameters, i.e. minimum support
(MinSup), minimum confidence (MinConf), number of
matching process or nRules, and number of iterations.
Below are the functions used in the program along with their
explanations.
• Aporiori_jalurter pendek
An apriori algorithm for shortest path problem in general
will be run by the aporiori_jalurterpendek function. This
function will summon other functions such as the parameters
used in the apriori namely, minimum support, minimum
confidence, n rules and iteration
The
program
summons
is
done
by
typing
“apriori_jalurterpendek” on the MATLAB Command
Window. The program will stop when the predetermined
generation limit has been met by users. An example of
program summons when entering data and outputs is: Type
“aporiori_jalurterpendenk” on the MATLAB command
window and press enter. The program will then go through a
running process as in figure 3.2

Figure 3.2 Apriori Running Process
The apriori_jalurterpendek process, during the running
process will generate output, as in figures 3.3 and 3.4

Figure 3.1 Research Design
The apriori algorithm for this case is as follows:
•
•
•
•
•

Determine the number of network nodes
Generate connection of each node/network using support
variable
Determine the value of each connection at each node,
with confidence variable
find the shortest node by generating the distance,
iteration, cost outputs
repeat step 2 if you want to use different number of nodes

3.2. Implementation

Figure 3.3. Best Solution Results of Apriori Algorithm

Figure 3.4 Overall Result of Apriori Algorithm
Figures 3.3 and 3.4 are the overall results of apriori algorithm.
Figure 3.3 shows the best solution results of apriori algorithm.
There are some colored lines indicating paths from data of
closest location, and there is a central point which can connect
to all location paths, at a total distance of 55.5802 and the
number of iterations is 2086 to reach an optimum level.
3.3 Results of Comparison Experiment
The experiments are done by changing the parameter
value of minimum confidence and support as well as the
iteration for all experiments. The experiment problem using
the problem of determining the solution optimality of apriori
algorithm will refert to the solution of genetic algorithm, since
genetic algorithm is widely used by other researchers in
determining the optimal solution to shortest path problem.
Below is the table of comparison between apriori algorithm
and genetic algorithm [2].

Figure 3.5 Best solutin results of apriori algorithm

Figure 3.6 Results of total apriori time
The next experiment result with large data is illustrated in the
following data:
Table 3 Comparsion Experiment of Genetic and Apriori
Algorithms (continued)

Algorithm
Genetika
Apriori

Numbe
r of
town
points
200
200

Source
node

Target
node

1
1

200
200

Optimal measure
iterati
Dista
Total
on
nce/c
time
ost
(second)
0.259
500
5931
58
4978
242.5

Table 3.1 Comparison Experiment of Genetic and Apriori
Algorithms

Algorithm
Genetic
Apriori

Numbe
r of
town
points
10
10

Source
node

Target
node

1
1

10
10

Optimal measure
iterati
Dista
Total
on
nce/c
time
ost
(second)
0.2
10
39
2
50
28

In table 3.1, two algorithms related to the material of finding
the shortest path with similar test parameters are tested. Using
the first test, the number of town points is 10, with source
node at 1 point, and target node in all points, i.e. 10 points.
The optimum measure is counted from the total time (second),
iteration, and distance/cost. In the first table, the genetic
algorithm is taken from Rama Sukaton’s, 2011, research
which has total time to obtain the shortest path with number of
iteration of 10 and distance or cost has a value of 39.
Meanwhile, the apriori algorithm delivers total time to obtain
the shortest path at 2 seconds, with number of iterations of 36
and distance/cost 26.

Figure 3.6 Result of iteration and distance/cost of apriori
algorithm
IV.

CONCLUSION AND SUGGESTION

This research proves that from execution time and
iteration perspective, genetic algorithm is far more superior,
while apriori algorithm is superior in its ability to determine
distance/cost. This algorithm can be used particularly to
reduce the costs spent to install new data network.
For further research, it is suggested to improve the ability
of finding the shortest path with apriori algorithm:

1.

2.

Another algorithm can be used to improve the optimum
to be a comparison of the more superior algorithm in
finding the solutions and shortest path
There is a need to add additional algorithms to awaken
the provision of support and confidence values to
guarantee that the apriori algorithm will not take to much
time and computation.
ACKNOWLEDGEMENT

This research was fully supported by Universitas Gunadarma,
Jakarta, Indonesia. The authors gratefully acknowledge
Universitas Gunadarma for providing research funding and for
permission in using the research facilities

REFERENCES
[1]

[2]

(R.Kumar dan M.Kumar, 2010). “Exploring Genetic Algorithm for
Shortest Path Optimization in Data Networks”, Global Journal of
Computer Science and Technology. Vol. 10 Issue 11 page 8-12 2010
Rama M Sukaton (2010), “Pengunaan Genetic algorithm Dalam
Masalah Jalur Terpedek Pada Data network”, Universitas Indonesia
2011

[3]

R. Agrawal and R. Srikant. “Fast, algorithms for mining association
rules in large databases”. Research Report RJ 9839, IBM Almaden
Research Center, San Jose, California, June 1994.
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