• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.93-104
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• 2005

The present article discusses the number of empty convex 4-gons and empty convex 5-gons in a finite planar point set. New proofs are provided for the two related important results.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.919-940
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• 2014

We conjecture that if $k{\geq}2$ is an integer and G is a graph of order n with minimum degree at least (n+2k)/2, then for any k independent edges $e_1$, ${\cdots}$, $e_k$ in G and for any integer partition $n=n_1+{\cdots}+n_k$ with $n_i{\geq}4(1{\leq}i{\leq}k)$, G has k disjoint cycles $C_1$, ${\cdots}$, $C_k$ of orders $n_1$, ${\cdots}$, $n_k$, respectively, such that $C_i$ passes through $e_i$ for all $1{\leq}i{\leq}k$. We show that this conjecture is true for the case k = 2. The minimum degree condition is sharp in general.

• Journal of IKEEE
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• v.5 no.1 s.8
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• pp.1-7
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• 2001

In this paper, we have investigated the CDMA(Code Division Multiple Access) Cellular System with non-linear equalizer in reverse link channel. In general, due to unknown characteristics of channel in the wireless communication, the distribution of the observables cannot be specified by a finite set of parameters; instead, we partitioned the m-dimensional sample space Into a finite number of disjointed regions by using quantiles and a vector quantizer based on training samples. The algorithm proposed is based on a piecewise approximation to regression function based on quantiles and conditional partition moments which are estimated by Robbins Monro Stochastic Approximation (RMSA) algorithm. The resulting equalizers and detectors are robust in the sense that they are insensitive to variations in noise distributions. The main idea is that the robust equalizers and robust partition detectors yield better performance in equiprobably partitioned subspace of observations than the conventional equalizer in unpartitioned observation space under any condition. And also, we apply this idea to the CDMA system and analyze the BER performance.

• The KIPS Transactions:PartA
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• v.14A no.7
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• pp.435-442
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• 2007

This paper is concerned with the mesh segmentation problem that can be applied to diverse applications such as texture mapping, simplification, morphing, compression, and shape matching for 3D mesh models. The mesh segmentation is the process of dividing a given mesh into the disjoint set of sub-meshes. We propose a method for segmenting meshes by simultaneously reflecting global and local geometric characteristics of the meshes. First, we extract sharp vertices over mesh vertices by interpreting the curvatures and convexity of a given mesh, which are respectively contained in the local and global geometric characteristics of the mesh. Next, we partition the sharp vertices into the $\kappa$ number of clusters by adopting the $\kappa$-means clustering method [29] based on the Euclidean distances between all pairs of the sharp vertices. Other vertices excluding the sharp vertices are merged into the nearest clusters by Euclidean distances. Also we implement the proposed method and visualize its experimental results on several 3D mesh models.

• The Transactions of the Korea Information Processing Society
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• v.7 no.2
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• pp.426-436
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• 2000

Given a linear arrangement of n base stations which generate multiple types of traffic among themselves, we consider the problem of finding a set of disjoint clusters to cover n base statons so that a cluster is assigned a location server. Our goal is to minimize the total communication cost for the entire network where the cost of intra-cluster communication is usually lower than that of intercluster communication for each type of traffic. The optimization problem is transformed into an equivavalent problem using the concept of relative cost, which generates the difference of communication costs between intracluster and intercluster communications. Using the relative cost matrix, an efficient algorithm of O($mm^2$), where m is the number of clusters in a partition, is designed by dynamic programming. The algorithm also finds all thevalid partitions in the same polynomial time, given the size constraint on a cluster, and the total allowable communication cost for the entire network.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1131-1131
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• 2001

To develop a nondestructive quality evaluation technique of fruits, a K-mean algorism is applied to near infrared (NIR) spectroscopy of apples. The K-mean algorism is one of neural network partition methods and the goal is to partition the set of objects O into K disjoint clusters, where K is assumed to be known a priori. The algorism introduced by Macqueen draws an initial partition of the objects at random. It then computes the cluster centroids, assigns objects to the closest of them and iterates until a local minimum is obtained. The advantage of using neural network is that the spectra at the wavelengths having absorptions against chemical bonds including C-H and O-H types can be selected directly as input data. In conventional multiple regression approaches, the first wavelength is selected manually around the absorbance wavelengths as showing a high correlation coefficient between the NIR $2^{nd}$ derivative spectrum and Brix value with a single regression. After that, the second and following wavelengths are selected statistically as the calibration equation shows a high correlation. Therefore, the second and following wavelengths are selected not in a NIR spectroscopic way but in a statistical way. In this research, the spectra at the six wavelengths including 900, 904, 914, 990, 1000 and 1016nm are selected as input data for K-mean analysis. 904nm is selected because the wavelength shows the highest correlation coefficients and is regarded as the absorbance wavelength. The others are selected because they show relatively high correlation coefficients and are revealed as the absorbance wavelengths against the chemical structures by B. G. Osborne. The experiment was performed with two phases. In first phase, a reflectance was acquired using fiber optics. The reflectance was calculated by comparing near infrared energy reflected from a Teflon sphere as a standard reference, and the $2^{nd}$ derivative spectra were used for K-mean analysis. Samples are intact 67 apples which are called Fuji and cultivated in Aomori prefecture in Japan. In second phase, the Brix values were measured with a commercially available refractometer in order to estimate the result of K-mean approach. The result shows a partition of the spectral data sets of 67 samples into eight clusters, and the apples are classified into samples having high Brix value and low Brix value. Consequently, the K-mean analysis realized the classification of apples on the basis of the Brix values.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.1
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• pp.22-37
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• 2013

Content distribution to a large number of concurrent clients stresses both server and network. While the server limitation can be circumvented by deploying server clusters, the network limitation is far less easy to cope with, due to the difficulty in measuring and balancing network load. In this paper, we use two useful network load metrics, the worst link stress (WLS) and the degree of interference (DOI), and formulate the problem as partitioning the clients into disjoint subsets subject to the server capacity constraint so that the WLS and the DOI are reduced for each session and also well balanced across the sessions. We present a network load-aware partition algorithm, which is practicable and effective in achieving the design goals. Through experiments on PlanetLab, we show that the proposed scheme has the remarkable advantages over existing schemes in reducing and balancing the network load. We expect the algorithm and performance metrics can be easily applied to various Internet applications, such as media streaming, multicast group member selection.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.195-201
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• 2007

A minimum terminal path decomposition of a tree is defined as a partition of the tree into edge-disjoint terminal-to-terminal paths that minimizes the weight of the longest path. In this paper, we present an $O({\mid}V{\mid}^2$time algorithm to find a minimum terminal path decomposition of trees. The algorithm reduces the given optimization problem to the binary search using the corresponding decision problem, the problem to decide whether the cost of a minimum terminal path decomposition is at most l. This decision problem is solved by dynamic programing in a single traversal of the tree.

• The KIPS Transactions:PartD
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• v.11D no.5
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• pp.1011-1020
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• 2004

A lot of work has been done to improve the I/O performance of such a system that store and manage a massive amount of data by distributing them across multiple disks and access them in parallel. Most of the previous work has focused on an efficient mapping from a grid ceil, which is determined bY the interval number of each dimension, to a disk number on the assumption that each dimension is split into disjoint intervals such that entire data space is GRID-like partitioned. However, they have ignored the effects of a GRID partitioning scheme on declustering performance. In this paper, we enhance the performance of mapping function based declustering algorithms by applying a good GRID par-titioning method. For this, we propose an estimation model to count the number of grid cells intersected by a range query and apply a GRID partitioning scheme which minimizes query result size among the possible schemes. While it is common to do binary partition for high-dimensional data, we choose less number of dimensions than needed for binary partition and split several times along that dimensions so that we can reduce the number of grid cells touched by a query. Several experimental results show that the proposed estimation model gives accuracy within 0.5% error ratio regardless of query size and dimension. We can also improve the performance of declustering algorithm based on mapping function, called Kronecker Sequence, which has been known to be the best among the mapping functions for high-dimensional data, up to 23 times by applying an efficient GRID partitioning scheme.