• The KIPS Transactions:PartB
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• v.15B no.6
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• pp.609-612
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• 2008

Let G = (V, E) be a simple undirected graph. The Minimum Vertex Cover (MVC) problem is to find a minimum subset C of V such that for every edge, at least one of its endpoints should be included in C. Like many other graph theoretic problems this problem is also known to be NP-hard. In this paper, we propose a genetic algorithm called LeafGA for MVC problem and show the performance of the proposed algorithm by applying it to several published benchmark graphs.

• Journal of the Korea Society of Computer and Information
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• v.16 no.7
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• pp.85-93
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• 2011

The Vertex Coloring Problem hasn't been solved in polynomial time, so this problem has been known as NP-complete. This paper suggests linear time algorithm for Vertex Coloring Problem (VCP). The proposed algorithm is based on assumption that we can't know a priori the minimum chromatic number ${\chi}(G)$=k for graph G=(V,E) This algorithm divides Vertices V of graph into two parts as independent sets $\overline{C}$ and cover set C, then assigns the color to $\overline{C}$. The element of independent sets $\overline{C}$ is a vertex ${\upsilon}$ that has minimum degree ${\delta}(G)$ and the elements of cover set C are the vertices ${\upsilon}$ that is adjacent to ${\upsilon}$. The reduced graph is divided into independent sets $\overline{C}$ and cover set C again until no edge is in a cover set C. As a result of experiments, this algorithm finds the ${\chi}(G)$=k perfectly for 26 Graphs that shows the number of selecting ${\upsilon}$ is less than the number of vertices n.

• Proceedings of the Korea Information Processing Society Conference
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• 2003.11b
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• pp.911-914
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• 2003

The prevention of D-Dos Attack requires to install filters at As border routers. This follows that finding minimum number of filters - VC(Vertex Cover), which is NP-complete problem. So, We propose improved 'Approximate VC' which is more efficient to real AS topology using topology property. Simulation shows that our algorithm, improved 'Approximated VC' enables us to reduce 25% VC nodes in comparison with 'Approximated VC'.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.3
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• pp.193-199
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• 2019

In this paper I propose an algorithm of linear time complexity for NP-complete Maximum Independent Set (MIS) problem. Based on the basic property of the MIS, which forbids mutually adjoining vertices, the proposed algorithm derives the solution by repeatedly selecting vertices in the ascending order of their degree, given that the degree remains constant when vertices ${\nu}$ of the minimum degree ${\delta}(G)$ are selected and incidental edges deleted in a graph of n vertices. When applied to 22 graphs, the proposed algorithm could obtain the MIS visually yet effortlessly. The proposed linear MIS algorithm of time complexity O(n) always executes ${\alpha}(G)$ times, the cardinality of the MIS, and thus could be applied as a general algorithm to the MIS problem.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.6
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• pp.183-191
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• 2011

This paper suggests emergency medical service vehicle (ambulance) algorithm when the emergency patient occurs in order to be sufficient the maximum permission time T of arrival about all sectors in one city that is divided in the various areas. This problem cannot be solved in polynomial times. One can obtains the solution using the integer programming. In this paper we suggest vertex set (or dominating set) algorithm and easily decide the location of ambulances. The core of the algorithm decides the location of ambulance is to the maximum degree vertex among the neighborhood of minimum degree vertex. For the 33 sectors Ostin city in Texas, we apply $3{\leq}T{\leq}20$ minutes. The traditional set cover algorithm with integer programming cannot obtains the solution in several T in 18 cases. But, this algorithm obtains solution for all of the 18 cases.