• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.181-192
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• 2003

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.427-432
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• 1998

When an undirected tree T and a vertex ${\gamma}$ in the tree are given the problem to transform T into a rooted tree with ${\gamma}$ as its root is considered. Using Euler tour and prefix sum an optimal algorithm has been developed [2,3]. We will present another parallel algorithm which is optimal also on EREW PRAM. Our approach resuces the given tree step by step by pruning and pointer jumping. That is the tree structure is retained during algorithm processing such that than other tree computations can be carried out in parallel.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.883-896
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• 2022

A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.899-910
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• 2019

In this paper, we enumerate the cardinalities for the set of all vertices of outdegree ${\geq}k$ at level ${\geq}{\ell}$ among all rooted ordered d-trees with n edges. Our results unite and generalize several previous works in the literature.

• Korean Journal of Computational Design and Engineering
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• v.13 no.3
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• pp.235-242
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• 2008

This paper proposes a method for improving the process plan quality by use of dimensional tolerances. Dimensioning and tolerancing plays a key role in manufacturing process plan because the final part must ensure conformance with the dimensions and tolerances in its drawing. As a first step for the improvement of process plan quality, two resultant tolerances in design and process plan should be compared each other, and so a tolerance chart is used for acquisition and comparison of the two tolerances. In addition to two kinds of design and manufacturing tolerances, operational sequences or paths for the resultant dimension and tolerance are additionally recognized for measuring the quality of process plan quantitatively. Rooted tree is applied to find the related paths for the manufacturing resultant tolerances. A quality coefficient is defined by the components of two tolerances and their relations, the paths related to manufacturing resultant tolerances and the difficulty of an operation. In order to improve the quality of manufacturing process plan, the paths that two kinds of tolerances are the same or different in the rooted tree are recognized respectively and a method for tolerance rearrangement is developed. A procedure for improving the quality is suggested by combining the coefficient and the tolerance rearrangement method. A case study is applied to illustrate the efficiency of improvement method.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.81-98
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• 1997

Given a rooted tree T with profits and node demands, the capacitated subtree of a tree problem (GSTP) consists of finding a rooted subtree of maximum profit, subject to having total demand no larger than the given capacity H. We first define the so-called critical item for CSTP and find an upper bound on the optimal value of CSTP in O(n$^{2}$) time, where n is the number of nodes in T. We then present our branch and bound algorithm for solving CSTP and illustrate the algiruthm by using an example. Finally, we implement our branch-and-bound algorithm and compare the computational results with those for both CPLEX and a dynamic programming algorithm. The comparison shows that our branch-and-bound algorithm performs much better than both CPLEX and the dynamic programming algorithm, where n and H are the range of [50, 500] and [5000, 10000], respectively.

• Journal of Environmental Science International
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• v.31 no.9
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• pp.735-741
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• 2022

Global warming affects forests and their ecology. Diversity in the forest is a buffer that reduces the damage due to global warming. Mixed forests are ecologically more valuable as versatile habitats and are effective in preventing landslides. In Korea, most forests were created by simple afforestation with trees of evergreen species. Typically, evergreen trees are shallow-rooted, and deciduous trees are deep-rooted. Mixed forest tree roots grip the soil effectively, which reduces the occurrence of landslides. Therefore, improving the distribution of tree types is essential to reduce damage due to global warming. For this improvement, the investigation of tree types of the forest is needed. However, determining the tree type distribution of forests that are spread over wide areas is labor-intensive and time-consuming. This study suggests effective methods for determining the distribution of tree types in a forest that is spread across a relatively wide area. Using normalized difference vegetation index and RGB images from unmanned aerial vehicles, each evergreen and deciduous tree, and grassland area can be distinguished. The distinguished image determines the distribution of tree type. This method is effective compared to directly determining the tree type distribution in the forest by the use of manpower. The data from these methods could be applied to plan a mixed forest or to prepare for future damage due to global warming.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.3
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• pp.485-498
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• 1996

For a tree T rooted at a concentrator location in a telecommunication system, we assume that the capacity H for the concentrator is given and a profit $c_v$, and a demand $d_v$, on each node $\upsilon$ of T are also given. Then, the capacitated subtree of a tree problem (CSTP) is to find a subtree of T rooted at the concentrator location so as to maximize the total profit, the sum of profits over the subtree, under the constraint satisfying that the sum of demands over the subtree does not exceed H. In this paper, we develop a pseudopolynomial-time algorithm for CSTP, the depth-first dynamic programming algorithm. We show that a CSTP can be solved by our algorithm in $\theta$ (nH) time, where n is the number of nodes in T. Our algorithm has its own advantage and outstanding computational performance incomparable with other approaches such as CPLEX, a general integer programming solver, when it is incorporated to solve a Local Access Telecommunication Network design problem. We report the computational results for the depth-first dynamic programming algorithm and also compare them with those for CPLEX. The comparison shows that our algorithm is competitive with CPLEX for most cases.

• Korean Journal of Environmental Agriculture
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• v.38 no.3
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• pp.154-158
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• 2019

BACKGROUND: 'Shiranuhi' mandarin is a major cultivar among all late ripening type of citrus, and is widely cultivated in Korea. However, many farmers have reported scion root problems in their orchard resulting in reduced flowering and fruiting. It is necessary that the physiology of scion-rooted 'Shiranuhi' mandarin trees is further understood. METHODS AND RESULTS: This experiment was conducted to understand the growth response and physiology of scion-rooted 'Shiranuhi' mandarin hybrids. In our study, 'Shiranuhi' mandarin trees were divided into two groups: trees without scion roots (control) and trees with scion roots. The experiment was conducted in Seogwipo of Jeju, with ten replicates for each group. Growth of trees with scion roots was more vigorous and the trees were taller than the controls. Tree height and trunk diameter of scion-rooted trees were significantly higher than those of control trees. Exposed length of rootstocks of scion-rooted trees was significantly lower (by about 2 cm) than that of control trees (8.6 cm). In terms of root nutrition, carbon contents of scion-rooted trees was significantly lower than that of control trees, but nitrogen and potassium concentrations in scion roots were significantly higher than those in control roots. CONCLUSION: Based on the results, we infer that growth of scion-rooted trees was very vigorous and the content of nitrogen in these roots was higher than that in the control tree roots. Thus, the carbon/nitrogen ratio of scion roots was significantly lower than that of the control roots.