• Journal of Institute of Control, Robotics and Systems
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• v.18 no.12
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• pp.1096-1100
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• 2012

Most of previous genetic algorithms for solving graph problems have used a vertex-based encoding. We proposed an edge encoding based new genetic algorithm using a spanning tree. Contrary to general edge-based encoding, a spanning tree-based encoding represents only feasible partitions. As a target problem, we adopted the MAX CUT problem, which is well known as a representative NP-hard problem, and examined the performance of the proposed genetic algorithm. The experiments on benchmark graphs are executed and compared with vertex-based encoding. Performance improvements of the spanning tree-based encoding on sparse graphs was observed.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.372-379
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• 2014

This paper surveys past and state-of-the-art SLAM technologies. The standard methods for solving the SLAM problem are the Kalman filter, particle filter, graph, and bundle adjustment-based methods. Kalman filters such as EKF (Extended Kalman Filter) and UKF (Unscented Kalman Filter) have provided successful results for estimating the state of nonlinear systems and integrating various sensor information. However, traditional EKF-based methods suffer from the increase of computation burden as the number of features increases. To cope with this problem, particle filter-based SLAM approaches such as FastSLAM have been widely used. While particle filter-based methods can deal with a large number of features, the computation time still increases as the map grows. Graph-based SLAM methods have recently received considerable attention, and they can provide successful real-time SLAM results in large urban environments.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.7
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• pp.448-453
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• 2006

We extend a parallel depth-first search (DFS) algorithm for planar graphs to deal with (non-planar) solid grid graphs, a subclass of non-planar grid graphs. The proposed algorithm takes time O(log n) with $O(n/sqrt{log\;n})$ processors in Priority PRAM model. In our knowledge, this is the first deterministic NC algorithm for a non-planar graph class.

• Journal of the Korean Society of Combustion
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• v.16 no.2
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• pp.16-22
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• 2011

It is a challenging task to apply large detailed chemical mechanisms of fuel oxidation in simulation of complex combustion phenomena. There exist a few systematic methodologies to reduce detailed chemical mechanisms to smaller sizes involving less computational load. This research work concerns generation of a skeletal chemical mechanism by a directed relation graph with specified accuracy requirement. Two sequential stages for mechanism reduction are followed in a perfectly stirred reactor(PSR) for high temperature chemistry and to consider the autoignition delay time for low and high temperature chemistry. Reduction was performed for the detailed chemical mechanism of n-heptane consisting of 561 species and 2539 elementary reaction steps. Validation results show acceptable agreement for the autoignition delay time and the PSR calculation in wide parametric ranges of pressure, temperature and equivalence ratio.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.703-722
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• 2021

Let G = (V, E) be a connected locally finite and weighted graph, ∆_p be the p-th graph Laplacian. Consider the p-th nonlinear equation -∆_pu + h|u|^p-2u = f(x, u) on G, where p > 2, h, f satisfy certain assumptions. Grigor'yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V. In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m-order differential operator 𝓛_m,p, we also prove the existence of the nontrivial solution to the analogous nonlinear equation.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.569-583
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• 2019

Given a graph G, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph G over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.911-926
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• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.133-147
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• 2024

Let G = (V, E) be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on G $${\Delta}u={\lambda}e^u(e^u-1)^5+4{\pi}\sum_{s=1}^{N}\delta_{ps}$$, where λ > 0, δ_ps is the Dirac mass at the vertex p_s, and p₁, p₂, . . . , p_N are arbitrarily chosen distinct vertices on the graph. We show that there exists a critical value $\hat{\lambda}$ such that when λ > $\hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when λ = $\hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when λ < $\hat{\lambda}$, the generalized Chern-Simons equation has no solution.

• Korean Institute of Interior Design Journal
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• v.18 no.5
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• pp.183-190
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• 2009

Increase in the elderly population has given rise to various social problems throughout Korean society, and what is more, although the greater demand of medical treatment, its development is still in its early stages. Given that Specialized Geriatrics Hospital has stood amid a range of spatial complication and it should faithfully reflect the needs of elderly population, we need a better understanding of Specialized Geriatrics Hospital. This study suggested the foundation to plan of Specialized Geriatrics Hospital through analyzing and evaluating spatial configuration of Specialized Geriatrics Hospital by "Space Syntax" and "J-Graph" The study focused on Specialized Geriatric Hospitals existing in Korea which owned more than 100 beds. The result of this study is summarized as follows; First, the rate of separated convex showed that the portions of the Treatment of outpatients and Supply have increased, but onthe other hand the portion of the The ward has been on the decrease. Second, in the case of Treatment of outpatients, it was structured Tree-shaped and the Tree-shaped could be separated with two types: waiting room and wailing room with lounge. in the case of The ward, it was structured Tree-shaped and also Ring-shaped. The more recently opened Geriatrics Hospital, the closer to Ring-shaped. Third, the access to the Ccentral treatment was low though the access to the core of the each floor was high. Fourth, in the progress of intelligibility, the fact that its value has decreased is becoming a serious problem of medical development for the elderly population finally, according to J-graph's analysis, the hallway made the spatial depth of rooms and public space more deepened. This caused by scattered arrangement of public spaces. As the only planning were considered in this study, It therefore needs more diversified approaches considering physical factors such like real distance and area.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.