• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.1-11
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• 2010

The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.977-986
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• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.4
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• pp.165-170
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• 2023

This paper proposes an algorithm that can obtain a solution with linear time for a set cover problem(SCP) in which there is no polynomial time algorithm as an NP-complete problem so far. Until now, only heuristic greed algorithms are known to select sets that can be covered to the maximum. On the other hand, the proposed algorithm is a competitive algorithm that applies an inclusion-exclusion principle rule to N nodes up to 2nd or 3rd in the maximum number of elements to obtain a set covering all k nodes, and selects the minimum cover set among them. The proposed algorithm compensated for the disadvantage that the greedy algorithm does not obtain the optimal solution. As a result of applying the proposed algorithm to various application cases, an optimal solution was obtained with a polynomial time of O(kn²).

• Proceedings of the Korean Geotechical Society Conference
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• 2005.10a
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• pp.564-569
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• 2005

Usually, Steel pipe grouting method or cut and cover method has been applied to tunnel with very shallow overburden or it is situated in valley. However, in case of lack of overburden height to reinforcement tunnel crown which is very difficult to construction. Also, application of cut and cover method that do not consider surrounding site condition causes popular enmity generation and environmental damage. It is the best alternative method that reduces the amount of excavated soil and excavate tunnel under ground to solve these problems. The tunneling method using cover structure which is to prevent a tunnel from collapse because this method can be reduce excavation area and construct tunnel under ground after set a cover structure and backfill ground. In this study, to know more effective structure type, comparative analysis was performed to behavior characters of slab and arch type construction that can be used to cover structure. Also a 2D and 3D numerical analysis have been performed to verify the stability of ground during excavation. As the result, the tunneling method using cover structure that it can be good alternative method for tunnel with shallow overburden and it through valley

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.511-512
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• 2003

The Terra/MODIS data set over Yellow River Basin, China is generated for the purpose of an input parameter into the water resource management model, which has been developed in the Research Revolution 2002 (RR2002) project. This dataset is mainly utilized for the land cover classification and radiation budget analysis. In this paper, the outline of the dataset generation, and a simple land cover classification method, which will be developed to avoid the influence of cloud contamination and missing data, are introduced.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.95-97
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• 1983

In this paper, we show a necessary and sufficient condition for QHC spaces to be S-closed. T. Thomson introduced S-closed spaces in [2]. A topological space X is said to be S-closed if every semi-open cover of X admits a finite subfamily such that the closures of whose members cover the space, where a set A is semi-open if and only if there exists an open set U such that U.contnd.A.contnd.Cl U. A topological space X is quasi-H-closed (denote QHC) if every open cover has a finite subfamily whose closures cover the space. If a topological space X is Hausdorff and QHC, then X is H-closed. It is obvious that every S-closed space is QHC but the converse is not true [2]. In [1], Cameron proved that an extremally disconnected QHC space is S-closed. But S-closed spaces are not necessarily extremally disconnected. Therefore we want to find a necessary and sufficient condition for QHC spaces to be S-closed. A topological space X is said to be semi-locally S-closed if each point of X has a S-closed open neighborhood. Of course, a locally S-closed space is semi-locally S-closed.

• Journal of Industrial Technology
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• v.4
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• pp.25-27
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• 1984

위상 공간 X의 모든 Semi-open cover에 대하여 그들의 closure의 합이 X를 cover한 유한 부분 속이 존재할 때 위상 공간X를 S-closed라고 한다. 이 논문에서는 S-closed와 semi-closed set 사이의 관계를 조사하였고 Haussdorff 공간과 S-closed 공간에서 extremally disconnected와 semi-continuous의 성질을 조사하였다.

• 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.

• Korean Journal of Remote Sensing
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• v.22 no.3
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• pp.199-209
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• 2006

The Global Land Cover 2000 (GLC 200) project, as a most recent issue, is to provide for the year 2000 a harmonized land cover database over the whole globe. The classifications were performed according to continental or regional scales by corresponding organization using the data of VEGETATION sensor onboard the SPOT4 Satellite. Even if the global land cover classification for Asia provided by Chiba University showed a good accuracy in whole Asian area, some problems were detected in Korean region. Therefore, the construction of new land cover database over Korea is strongly required using more recent data set. The present study focuses on the development of a new upgraded land cover map at 1 km resolution over Korea considering the widely used K-means clustering, which is one of unsupervised classification technique using distance function for land surface pattern classification, and the principal components transformation. It is based on data sets from the Earth observing system SPOT4/VEGETATION. Newly classified land cover was compared with GLC 2000 for Korean peninsula to access how well classification performed using confusion matrix.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.121-134
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• 2008

A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The covering cover pebbling number of a graph is the smallest number of pebbles, such that, however the pebbles are initially placed on the vertices of the graph, after a sequence of pebbling moves, the set of vertices with pebbles forms a covering of G. In this paper we find the covering cover pebbling number of n-cube and diameter two graphs. Finally we give an upperbound for the covering cover pebbling number of graphs of diameter d.