• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.219-233
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• 1994

A fixed k-coloring problem is introduced and dealt with by efficient heuristic algorithms. It is shown that the problem can be transformed into the graph partitioning problem. Initial coloring and improving methods are proposed for problems with and with and without the size restriction. Algorithm Move, LEE and OEE are developed by modifying the Kernighan-Lin's two way uniform partitioning procedure. The use of global information in the selection of the node and the color set made the proposed algorithms superior to the existing method. The computational result also shows that the superiority does not sacrifice the time demand of the proposed algorithms.

• Proceedings of the Korea Information Processing Society Conference
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• 2003.05a
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• pp.527-530
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• 2003

In this paper, we implemented the voxel coloring method to reconstruct 3D object from synthetic input Images. Then compare the result between using standard voxel coloring and using coarse-to-fine method. We compared using different voxel space site to see the difference of time processing and the result of 3D object. Photorealistic 3D object reconstruction is a challenging problem in computer graphics. Vexel coloring considered the reconstruction problem as a color reconstruction problem, instead of shape reconstruction problem. This method works by discretizing scene space into yokels, then traversed and colored those in special order. Also there is an extension of voxel coloring method far decreasing the amount of processing time called coarse-to-fine method. This. method works using low resolution instead of high resolution as input and after processing finish, apply some kind of search strategy.

• Journal of Korean Institute of Industrial Engineers
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• v.18 no.2
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• pp.43-49
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• 1992

Edge coloring problem is to find a minimum cardinality coloring of the edges of a graph so that any pair of edges incident to a common node do not have the same colors. Edge coloring problem is NP-hard, hence it is unlikely that there exists a polynomial time algorithm. We formulate the problem as a covering of the edges by matchings and find valid inequalities for the convex hull of feasible solutions. We show that adding the valid inequalities to the linear programming relaxation is enough to determine the minimum coloring number(chromatic index). We also propose a method to use the valid inequalities as cutting planes and do the branch and bound search implicitly. An example is given to show how the method works.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.35-49
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• 1993

The node coloring problem is a problem to color the nodes of a graph using the minimum number of colors possible so that any two adjacent nodes are colored differently. This problem, along with the edge coloring problem, has a variety of practical applications particularly in item loading, resource allocation, exam timetabling, and channel assignment. The node coloring problem is an NP-hard problem, and thus many researchers develop a number of heuristic algorithms. In this paper, we survey and classify those heuristics with the emphasis on how an algorithm orders the nodes and colors the nodes using a determined ordering.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.2
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• pp.226-232
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• 1999

Graph Coloring Problem(GCP) is a problem of assigning different colors to nodes which are connected by an edge. An extended form of GCP is TCP (T-coloring problem) and, in TCP, edge weights are added to GCP and it is possible to extend GCP's applications. To solve TCP, in this paper, we propose an improved Simulated Annealing(SA) method with search space smoothing. It has been observed that the improved SA method obtains better results than SA does.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• The Journal of the Korea Contents Association
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• v.14 no.10
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• pp.840-849
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• 2014

The paper shows that algorithm education positively affects algorithmic thinking for elementary students. Experiments are conducted on thirty five sixth graders without prior experience of algorithm. The experimental group is given eleven sessions of lesson for four weeks in which algorithmic solution is sought for graph coloring problems. After four weeks of experiments questionnaires are distributed to the students in order to measure differences in algorithmic interest and algorithmic thinking ability. The following results are obtained: Firstly, it may be observed that algorithm education with graph coloring may be effective in reinforcing students' interest in algorithms. Secondly, the experiment shows that algorithmic thinking ability may be enhanced from participating in graph coloring activities. In conclusion, algorithm education with graph coloring problem helps students develop algorithmic thinking ability as well as cultivate students' interest in algorithmic thinking.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1375-1377
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• 2002

New graph coloring problems are discussed as models of a multihop network in this report. We consider a total scheduling problem, and prove that this problem is NP-hard. We propose new scheduling models of a multi-hop network for CDMA system, and show the complexity results of the scheduling problems.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10b
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• pp.79-81
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• 2001

그래프 착색 문제(Graph Coloring Problem)는 인접한 노드 (V$_{i}$, V$_{j}$ )가 같은 색을 갖지 않도록 그래프 G의 노드 V에 색을 배정하는 문제로, NP-hard 문제로 잘 알려져 있다. 또한 최근까지 그래프 착색 문제의 최적 해를 구하기 위하여 다양한 접근방식들과 해법들이 제안되고 있다. 본 논문에서는 기존의 그래프 착색 문제의 해법으로 잘 알려진 Greedy algorithms, Simulated Annealing. Tabu search 등이 아닌 실세계에서 개미들이 자신의 분비물을 이용하여 경로를 찾는 Ant System을 개선하여 새롭게 제안한 Ant Colony System(ACS) 알고리즘으로 해를 구하는 ANTCOL을 소개하고, ANTCOL에서 DSATUR, Recursive Largest First(RLF) 등의 방식을 사용한 기존 생성 함수들과 RLF를 개선하여 제안한 eXtend RLF방식을 사용한 생성 함수를 비교, 평가하고자 한다.