• Korean Journal of Mathematics
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• v.20 no.2
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• pp.255-261
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• 2012

Let $\mathcal{O}_n$ be the set of ordered labeled trees on $\{0,\;{\ldots},\;n\}$. A maximal decreasing subtree of an ordered labeled tree is defined by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{O}_{n,k}$ of $\mathcal{O}_n$, which is the set of ordered labeled trees whose maximal decreasing subtree has $k+1$ vertices.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1247-1263
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• 2019

In ordered trees, two randomly chosen vertices are said to be dependent if one lies under the other. If not, we say that they are independent. We consider several classes of ordered trees with uniform updegree requirements and find the generating functions for the trees with two marked dependent/independent vertices. As a result, we compute the probability for two vertices being dependent/independent. We also count such trees by the distance between two independent vertices.

• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.2
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• pp.169-176
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• 2000

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with primary concern of minimizing link congestion. The authors showed that a complete binary tree with $2^P-1$ nodes can be embedded into a 3-dimensional mesh with optimum size, $2^P$ nodes, if the link congestion is two[14], (More precisely, the link congestion of each dimension is two, two, and one if the dimension-ordered routing is used, and two, one, and one if the dimension-ordered routing is not imposed.) In this paper, we present a scheme to find an embedding of a complete binary tree into a 3-dimensional mesh of size no larger than 1.27 times the optimum with link congestion one while using dimension-ordered routing.

• ETRI Journal
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• v.33 no.3
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• pp.344-354
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• 2011

In this paper, a model is introduced named double relation chains (DRC) based on ordered sets. It is proved that using DRC and special relationships among the members of an alphabet, vectors of this alphabet can be stored and searched in a tree. This idea is general; however, one special application of DRC is the longest prefix matching (LPM) problem in an IP network. Applying the idea of DRC to the LPM problem makes the prefixes comparable like numbers using a pair of w-bit vectors to store at least one and at most w prefixes, where w is the IP address length. This leads to good compression performance. Based on this, two recently introduced structures called coded prefix trees and scalar prefix trees are shown to be specific applications of DRC. They are implementable on balanced trees which cause the node access complexity for prefix search and update procedures to be O(log n) where n is the number of prefixes. As another advantage, the number of node accesses for these procedures does not depend on w. Additionally, they need fewer number of node accesses compared to recent range-based solutions. These structures are applicable on both IPv4 and IPv6, and can be implemented in software or hardware.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.381-386
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• 2003

In this paper, we consider the problem of embedding complete binary trees into 3-dimensional meshes. The method of embedding a complete binary tree into 3-dimensional mesh with the link congestion two is considered in [1], and the embedding in [2] shows that a complete binary tree can be embedded into a ,3-dimensional mesh of expansion 1.27. The proposed embedding in this paper shows that a complete binary tree can be embedded into a 3-dimensional mesh of expansion approximately 1.125 with the link congestion one, using the dimensional ordered routing. Such method yields some improved features in terms of minimizing the link congestion or the expansion of embedding comparing to the previous results.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.187-199
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• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $b^{(r)}_n$ and $b^{(r+1)}_n$.

• International Journal of Highway Engineering
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• v.18 no.6
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• pp.173-180
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• 2016

OBJECTIVES : Fixed roadside objects are a threat to drivers when their vehicles deviate from the road. Therefore, such roadside objects need to be suitably dealt with to decrease accidents. This study determines the factors affecting the severity of accidents because of fixed roadside objects. METHODS : This study analyzed the crash severity impact of fixed roadside objects by using ordered probit regression as the analysis methodology. In this research, data from 896 traffic accidents reported in the last three years were used. These accidents consisted of sole-car accidents, fixed roadside object accidents, and lane-departure accidents on the national highway of Korea. The accident severity was classified as light injury, severe injury, and death. The factors relating to the road and the driver were collected as independent variables. RESULTS : The result of the analysis showed that the variables of the crash severity impact are the collision location (left side), gender of the driver (female), alcohol use, collision facility (roadside trees, traffic signals, telephone poles), and type of road (rural segments). Additionally, the collision location (left side), gender of the driver (female), alcohol use, collision facility (street trees, traffic signals, telephone poles), and type of road (rural segments), in order of influence, were found to be the factors affecting the crash severity in accidents due to fixed roadside objects. CONCLUSIONS : An alternative solution is urgently required to reduce the crash severity in accidents due to fixed roadside objects. Such a solution can consider the appropriate places to install breakaway devices and energy-absorbing systems.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.4
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• pp.233-241
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• 2014

This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge (e) per vertex (v). Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform |e| times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until |e|=|v|-1 For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.

• The Transactions of the Korea Information Processing Society
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• v.7 no.6
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• pp.1956-1963
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• 2000

In this paper, a wavelet image coding scheme exploiting the correlation of neighboring VQ indices in eh wavelet domain is proposed. the codewords in each sub-codebook are re-ordered in terms of their energies in order to increase the correlation of he indices. Then, the generated indices after VQ can be further encoded by non-adaptive DPCM/Huffman method. LBG algorithm and a fast-PNN algorithm using k-d trees are used for generating a multiresolution codebook. Experimental results show that or scheme outperforms the ordinary wavelet VQ and JPEG at low bit rates.