• 제어로봇시스템학회논문지
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• 제16권1호
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• pp.48-52
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• 2010

In this paper, we introduce a new path planning algorithm which combines the merits of a visibility graph algorithm and an adaptive cell decomposition. We quantize a given map with empty cells, blocked cells, and mixed cells, then find the optimal path on the quantized map using a visibility graph algorithm. For reducing the number of the quantized cells we use the quad-tree technique which is used in an adaptive cell decomposition, and for improving the performance of the visibility checking in making a visibility graph we propose a new visibility checking method which uses the property of the quad-tree instead of the well-known rotational sweep-line algorithm. For the more efficient visibility checking, we propose two additional improvements for our suggested method. Both of them are used for reducing the visited cells in the quad-tree. The experiments for a performance comparison of our algorithm with other well-known algorithms show that our proposed method is superior to others.

• 대한수학회지
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• 제53권5호
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• Nuclear Engineering and Technology
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• 제54권8호
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• pp.2859-2870
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• 2022

Because nuclear power plants (NPPs) are safety-critical infrastructure, it is essential to increase their safety and minimize risk. To reduce human error and support decision-making by operators, several artificial-intelligence-based diagnosis methods have been proposed. However, because of the nature of data-driven methods, conventional artificial intelligence requires large amount of measurement values to train and achieve enough diagnosis resolution. We propose a graph neural network (GNN) based accident diagnosis algorithm to achieve high diagnosis resolution with limited measurements. The proposed algorithm is trained with both the knowledge about physical correlation between components and measurement values. To validate the proposed methodology has a sufficiently high diagnostic resolution with limited measurement values, the diagnosis of multiple accidents was performed with limited measurement values and also, the performance was compared with convolution neural network (CNN). In case of the experiment that requires low diagnostic resolution, both CNN and GNN showed good results. However, for the tests that requires high diagnostic resolution, GNN greatly outperformed the CNN.

• 대한수학회지
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• 제59권4호
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• pp.757-774
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• 2022

Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), d_H(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ₂(G) = min_uv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ₂(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ₂(G) is sharp.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• 대한수학회보
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• 제58권5호
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• pp.1279-1300
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• 2021

Let P be a finite point set in ℝ² with the set of distance n-chains defined as ∆_n(P) = {(|p₁ - p₂|, |p₂ - p₃|, …, |p_n - p_n+1|) : p_i ∈ P}. We show that for 2 ⩽ n = O_|P|(1) we have ${\mid}{\Delta}_n(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^n}{{\log}^{\frac{13}{2}(n-1)}{\mid}P{\mid}}}$. Our argument uses the energy construction of Elekes and a general version of Rudnev's rich-line bound implicit in [28], which allows one to iterate efficiently on intersecting nested subsets of Guth-Katz lines. Let G is a simple connected graph on m = O(1) vertices with m ⩾ 2. Define the graph-distance set ∆_G(P) as ∆_G(P) = {(|p_i - p_j|)_{i,j}∈E(G) : p_i, p_j ∈ P}. Combining with results of Guth and Katz [17] and Rudnev [28] with the above, if G has a Hamiltonian path we have ${\mid}{\Delta}_G(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^{m-1}}{\text{polylog}{\mid}P{\mid}}}$.

• 한국항만학회지
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• 제12권1호
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• pp.55-64
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• 1998

본 논문은 Crandall의 탑승자 사망에 관한 모형에 Directed Graph를 응용한 것으로써 데이터는 Crandall이 사용한 미국의 1947-1981 기간의 탑승자 사망 데이터를 1993년까지 확장한 것을 사용하였다. Directed Graph Algorithm방법은 최근에 컴퓨터과학 분야에서 발전된 것을 원용한 것이다. 먼저 1947-1981 기간의 데이터를 기초로 하여 회귀분석을 통한 분석 대신에 Directed Graph Algorithm을 이용한 결과, 회귀분석을 이용했던 Crandall의 결과와는 달리 탑승자 사망은 소득수준, 자동차의 운행거리, 자동차의 안전장치 수준에 의하여 직접적으로 결정이 되는 것으로 나타났다. 자동차의 운행거리는 수득수준과 시내주행에 대한 교외주행 의 비 에 의해서 결정되는 것으로 나타났다. 이런 결과에 근거하여 3SLS(three stage least squares regression)를 이용하여 추정하고, 이러한 추정에 근거하여 1982-1993 기간을 예측했으며, Crandall의 원래의 모형의 예측력과 비교를 하여？. 예측 결과 본 모형이 MSE(mean squared error)를 기준으로한 예측력에서 훨씬 뛰어난 결과를 보였다. 더욱 중요한 것은 본고에서는 Crandall이 사용한 변수간에 기존의 계량적 방법으로는 색출이 불가능했던 잠재변수 (Latent variable)가 존재함을 구체적으로 보임으로써 회귀분석을 통한 모형화는 진정한 변수간의 관계를 반영치 못함을 보인 것이다.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• 정보처리학회논문지B
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• 제11B권2호
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• pp.221-226
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• 2004

개미 집단 시스템(Ant Colony System ACS) 알고리즘은 조합 최적화 문제를 해결하기 위한 새로운 메타 휴리스틱 방법이다. 이것은 그리디 탐색뿐만 아니라 긍정적 피드백에 의한 탐색을 이용한 모집단에 근거한 접근법으로 조합 최적화 문제를 해결하기 위해 제안되었다. 최근까지 인접한 노드($v_i, v_j$)가 같은 색을 갖지 않도록 그래프 G의 노드 V에 색을 배정하는 문제인 그래프 착색 문제의 최적 해를 구하기 위하여 다양한 접근 방식들과 해법들이 제안되고 있다. 본 논문에서는 기존의 그래프 착색 문제의 해법으로 잘 알려진 그리디 알고리즘, 시뮬레이티드어넬링, 타부 탐색 등이 아닌 개미 집단 시스템 알고리즘으로 해법을 구하는 방법인 ANTCOL 알고리즘을 소개하고, ANTCOL을 해결하기 위해 제안된 기존의 생성 함수들(ANT_Random ANT_LF, ANT_SL, ANT_DSATUR, ANT_RLF)과, 본 논문에서 새롭게 제안된 방법으로 RLF에 무작위 기법을 적용한 XRLF를 생성 함수로 사용한 ANT_XRLF 방법과 ANT_XRLF에 재검색을 추가한 방법(ANT_XRLF_R)의 그래프 착색 결과 및 실행 시간을 비교, 분석하여 제안된 방법이 더 빠르게 수렴할 수 있음을 실험을 통해 알 수 있었다.

• 한국생물정보학회:학술대회논문집
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• 한국생물정보시스템생물학회 2005년도 BIOINFO 2005
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• pp.228-233
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• 2005

The protein side-chain packing problem (SCPP) is known to be NP-complete. Various graph theoretic based side-chain packing algorithms have been proposed. However as the size of the protein becomes larger, the sampling space increases exponentially. Hence, one approach to cope with the time complexity is to decompose the graph of the protein into smaller subgraphs. Some existing approaches decompose the graph into biconnected components at an articulation point (resulting in an at-most 21-residue subgraph) or solve the SCPP by tree decomposition (4-, 5-residue subgraph). In this regard, we had also presented a deterministic based approach called as SPWCQ using the notion of maximum edge weight clique in which we reduce SCPP to a graph and then obtain the maximum edge-weight clique of the obtained graph. This algorithm performs well for a protein of less than 500 residues. However, it fails to produce a feasible solution for larger proteins because of the size of the search space. In this paper, we present a new heuristic approach for the side-chain packing problem based on the maximum edge-weight clique finding algorithm that enables us to compute the side-chain packing of much larger proteins. Our new approach can compute side-chain packing of a protein of 874 residues with an RMSD of 1.423${\AA}$.