Aveneu Park, Starling, Australia

1: center problem to find optimal solution. He also

1: Abstract:

From many decades, there
are large numbers of searches which are made on facility problems. The k-center
problem is a very common problem in public or private sector. There are many
efforts which have been made for optimal solution of this nature problem. The
point of this paper is to draw an attention on algorithmic approach which has
been in that area. In future, new researches on this topic will be made.

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2: Introduction:

K center algorithms (greedy
algorithms) are a way to make a summarized connection from an origin to a
destiny. It is like centralized a destiny from certain points, that the point
can get benefit from it. Facility location problem is a very well known
problem, suppose the given no. of cities and distances between cities, we want
to choose k cities which is also called center. In that case we minimized the
distance between center and the largest distance city.

 

 

Figure 1:

As we can see that {4,3,10,11,13} are the five point that we
pick from {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} , the five points we picked are
the centralized points , through all the other points can b interact easily and
have short path to get the needy things.

 

3:
Literature review:

In computer science and operation research literature,
k-center problem got highly attention. Hockbaum and Shmoys (1985) proposed 2
approximate algorithms of k center problem with triangle inequality.

After Hocbaum and Shmoys, J Plesnik in 1987 gathered
the results, with the worst case error ratio of 2 is developed for p center
problem.

After that Daskin modified those algorithms of p
center problem to find optimal solution. He also presents a new model for k
center problem in 2000.

In 2005 Al Khedhairi modified those old algorithms
to solve the k center problem, he speed up that process of solving the k center
problem.

 

4:
Methodology (Explanation of algorithm):

GreedyKCenter(P, k) {

G = empty

for each u in P do // initialize distances

du = INFINITY

for (i = 1 to k) {

Let u be the point of P such that du is maximum

Add u to G // u is the next cluster center

for (each v in P) { // update distance to nearest
center

dv = min(dv, distance(v,u))

}

Delta = max_{v in P} dv // update the bottleneck
distance

}

return (G, Delta) // final centers and max distance

}

Figure 2:

As we can see that, from the center point we draw a
line which is called radius, through this we made circumference, and that
circumference cover the near points, that center is like a warehouse, and the
other points the things that they need. The circumference that we made contain
the points that have smallest path from the center, and easy to cover the
distance.

5: Analysis and Comparison with other algo’s solving same
problem:

6: Major finding:

 

 

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