• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.57-70
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• 2002

This work presents an iterative mesh partitioning approach to improve the efficiency of parallel substructure finite element computations. The proposed approach employs an iterative strategy with a set of empirical rules derived from the results of numerical experiments on a number of different finite element meshes. The proposed approach also utilizes state-of-the-art partitioning techniques in its iterative partitioning kernel, a cost function to estimate the computational cost of each submesh, and a mechanism that adjusts element weights to redistribute elements among submeshes during iterative partitioning to partition a mesh into submeshes (or substructures) with balanced computational workloads. In addition, actual parallel finite element structural analyses on several test examples are presented to demonstrate the effectiveness of the approach proposed herein. The results show that the proposed approach can effectively improve the efficiency of parallel substructure finite element computations.

• KIISE Transactions on Computing Practices
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• v.21 no.11
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• pp.681-688
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• 2015

The k nearest neighbor (k-NN) graph construction is an important operation with many web-related applications, including collaborative filtering, similarity search, and many others in data mining and machine learning. Despite its many elegant properties, the brute force k-NN graph construction method has a computational complexity of $O(n^2)$, which is prohibitive for large scale data sets. Thus, (Key, Value)-based distributed framework, MapReduce, is gaining increasingly widespread use in Locality Sensitive Hashing which is efficient for high-dimension and sparse data. Based on the two-stage strategy, we engage the locality sensitive hashing technique to divide users into small subsets, and then calculate similarity between pairs in the small subsets using a brute force method on MapReduce. Specifically, generating a candidate group stage is important since brute-force calculation is performed in the following step. However, existing methods do not prevent large candidate groups. In this paper, we proposed an efficient algorithm for approximate k-NN graph construction by regrouping candidate groups. Experimental results show that our approach is more effective than existing methods in terms of graph accuracy and scan rate.

• The Journal of Korean Association of Computer Education
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• v.9 no.6
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• pp.41-51
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• 2006

Educators have recognized the usefulness of the e-BBS(electronic-Bulletin Board System) as an asynchronous communication medium for collaborative learning. However, theoretical outcomes to understand the structural analysis of thc e-BBS are not adequate enough. As a consequence, we are left with inadequate supportive tools to understand complex communication phenomena and to assist teachers to guide students to educational purposes. This can cause teachers to have a laissez-faire approach using BBS as a communication medium for education due to the lack of understanding the structural and overall situation. To address this issue, this paper presents a theoretical foundation to help understand the structure of discussion activities via the e-BBS and then presents a computational model, based on the structural analysis, for the behavioral analysis of participants. The formal representation of bi-directional discussion activities is realized by devising two graphs - the reply graph and the connection graph. Various measurements and statistics for the analysis are presented in the paper. To clarify the analysis, we classify the results produced through the analysis of discussion activities and participants' behaviors.

• The Journal of the Korea Contents Association
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• v.16 no.12
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• pp.1-9
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• 2016

Computational Fluid Dynamics(CFD) is a branch of fluid mechanics that solves partial differential equations which represent fluid flows by a set of algebraic equations using computers. Even though it requires multifarious variables, only selected ones are stored because of the lack of storage capacity. It causes the requirement of secondary variable calculations at analyzing time. In this paper, we suggest an efficient method to estimate optimal calculation paths for secondary variables. First, we suggest a converting technique from a dependency graph to a ordinary directed graph. We also suggest a technique to find the shortest path from any initial variables to target variables. We applied our method to a tool for data analysis and visualization to evaluate the efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.383-388
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• 2007

A (g, f)-factor F of a graph G is Called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. The binding number of G is defined by $bind(G)\;=\;{min}\;\{\;{\frac{{\mid}N_GX{\mid}}{{\mid}X{\mid}}}\;{\mid}\;{\emptyset}\;{\neq}\;X\;{\subset}\;V(G)},\;{N_G(X)\;{\neq}\;V(G)}\;\}$. Let G be a connected graph, and let a and b be integers such that $4\;{\leq}\;a\;<\;b$. Let g, f be positive integer-valued functions defined on V(G) such that $a\;{\leq}\;g(x)\;<\;f(x)\;{\leq}\;b$ for every $x\;{\in}\;V(G)$. In this paper, it is proved that if $bind(G)\;{\geq}\;{\frac{(a+b-5)(n-1)}{(a-2)n-3(a+b-5)},}\;{\nu}(G)\;{\geq}\;{\frac{(a+b-5)^2}{a-2}}$ and for any nonempty independent subset X of V(G), ${\mid}\;N_{G}(X)\;{\mid}\;{\geq}\;{\frac{(b-3)n+(2a+2b-9){\mid}X{\mid}}{a+b-5}}$, then G has a Hamiltonian (g, f)-factor.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.447-460
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• 2006

This paper develops a multiple comparison method for finding an optimal ordering of K geometric means of exponential parameters. This is based on the paired comparison experimental arrangement whose results can naturally be represented by a completely oriented graph. Introducing posterior preference probabilities and stochastic transitivity conditions to the graph, we obtain a new graphical model that yields criteria for the optimal ordering in the multiple comparison. Necessary theories involved in the method and some computational aspects are provided. Some numerical examples are given to illustrate the efficiency of the suggested method.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.173-181
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• 2006

In this paper, an integration framework of Geometric Constraint Solving Engine and AutoCAD is presented, and a dynamic geometric constraint system is introduced. According to inherent orientation features of geometric entities and various Object Snap results of AutoCAD, the' proposed system can automatically construct an under-constrained geometric constraint model during interactive drawing. And then the directed constraint graph in a geometric constraint model is realtime modified in order to produce an optimal constraint solving sequence. Due to the open object-oriented characteristics of AutoCAD, a set of user-defined entities including basic geometric elements and graphics constraint relations are defined through derivation. And the custom-made Object Reactor and Command Reactor are also constructed. Several powerful characteristics are achieved based on these user-defined entities and reactors, including synchronously processing geometric constraint information while saving and opening DWG files, visual constraint relations, and full adaptability to Undo/Redo operations. These characteristics of the proposed system can help the designers more easily manage geometric entities and constraint relations between them.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.21-38
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• 2006

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.39-49
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• 2004

Let G be a simple graph and let $\={G}$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. If $\overline{aK_{a}\;{\bigcup}\;{\beta}K_{b}}$ is integral we show that it belongs to the class of integral graphs $[\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;z}\;K_{(t+{\ell}n)+{\ell}m}\;\bigcup\;[\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t\;+\;{\ell}n)k\;+\;{\ell}m}{\tau}\;z]n\;K_{em)$, where (i) t, k, $\ell$, m, $n\;\in\;\mathbb{N}$ such that (m, n) = 1, (n,t) = 1 and ($\ell,\;t$) = 1 ; (ii) $\tau\;=\;((t\;+\;{\ell}n)k\;+\;{\ell}m,\;mt)$ such that $\tau\;$\mid$kt$; (iii) ($x_0,\;y_0$) is a particular solution of the linear Diophantine equation $((t\;+\;{\ell}n)k\;+\;{\ell}m)x\;-\;(mt)y\;=\;\tau\;and\;(iv)\;z\;{\geq}\;{z_0}$ where $z_{0}$ is the least integer such that $(\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;{z_0})\;\geq\;1\;and\;(\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t+{\ell}n)k+{\ell}m}{\tau}\;{z_0})\;\geq\;1$.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.