• Journal of the Society of Naval Architects of Korea
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• v.59 no.6
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• pp.393-399
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• 2022

During the ship hull design process, resistance performance estimation is generally calculated by simulation using computational fluid dynamics. Since such hull resistance performance simulation requires a lot of time and computation resources, the time taken for simulation is reduced by CPU clusters having more than tens of cores in order to complete the hull design within the required deadline of the ship owner. In this paper, we propose a method for estimating resistance performance of ship hull by simulation using a graph neural network. This method converts the 3D geometric information of the hull mesh and the physical quantity of the surface into a mathematical graph, and is implemented as a deep learning model that predicts the future simulation state from the input state. The method proposed in the resistance performance experiment of simple hull showed an average error of about 3.5 % throughout the simulation.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.123-129
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• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• East Asian mathematical journal
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• v.30 no.3
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• pp.311-319
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• 2014

It is shown that, for an even positive integer m with $m{\geq}4$ and arbitrary positive integer k and t, the complete multipartite graph $K_{km+1(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles in such a way that the decomposition is circulant.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.317-329
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• 2022

In this paper we investigate the pair difference cordial labeling behaviour of m- copies of K₄, subdivision of star, fan, comb graphs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.2
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• pp.228-234
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• 2006

This paper describes a systematic process which can generate a complete circuit specification efficiently for a given recursive DSP algorithm based on an optimal multiprocessor scheduler. The process is composed of two states: scheduling and circuit synthesis. The scheduling part accepts a fully specified flow graph(FSFG) as an input, and generates an optimal synchronous multiprocessor schedule. Then the circuit synthesis part translates the modified schedule into a complete circuit diagram including a control specification. The circuit diagram can be applied to a silicon compiler for VLSI layout generation. This paper illustrates the whole process with an example of a second order Gray-Market lattice filter.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.11
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• pp.830-835
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• 2006

Because of its exponential growth of data and voice transmissions through wireless communications, efficient resource management became more important factor when we design wireless networks. One of those limited resources in the wireless communications is frequency bandwidth. As a solution of increasing reusability of resources, the efficient frequency assignment problems on wireless networks have been widely studied. One suitable approach to solve these frequency assignment problems is transforming the problem into traditional graph coloring problems in graph theory. However, most of frequency assignments on arbitrary network topology are NP-Complete problems. In this paper, we consider the Chromatic Bandwidth Problem on the cellular topology wireless networks. It is known that the lower bound of the necessary number of frequencies for this problem is $O(k^2)$. We prove that the lower bound of the necessary number of frequencies for the Chromatic Bandwidth Problem is $O(k^3)$ which is tighter lower bound than the previous known result.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.4
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• pp.253-258
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• 2003

We consider the problem of grouping orders into lots. The problem is modelled by a graph G=(V,E), where each node ${\nu}{\in}V$ denotes order specification and its weight ${\omega}(\nu)$ the orders on hand for the specification. We can construct a lot simply from orders of single specification. For a set of nodes (specifications) ${\theta}{\subseteq}V$, if the distance of any two nodes in $\theta$ is at most d, it is also possible to make a lot using orders on the nodes. The objective is to maximize the number of lots with size exactly $\lambda$. In this paper, we prove that our problem is NP-Complete when $d=2,{\lambda}=3$ and each weight is 0 or 1. Moreover, it is also shown to be NP-Complete when $d=1,{\lambda}=3$ and each weight is 1,2 or 3.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7B
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• pp.1239-1251
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• 1999

In this paper a scalable QoS-based hierarchical inter-domain routing scheme for distributed multimedia applications in a high speed wide area network. The problem of QoS-based routing is formulated as a multicriteria shortest path problem, known as NP-complete[21,30]. Our routing scheme consists of two phases. In Phase 1, two graph construction algorithms are performed to model the network under consideration as a graph. The graph contains a part of the network topology which is completely neglected or partially considered by existing routing schemes, thus maintaining more accurate topology information. In Phase 2, a heuristic call-by-call algorithm is performed for selecting a feasible path efficiently in depth first search-like manner on the graph and tailoring to each application's QoS requirements, beginning at a vertex that represents the source node. In this paper, a simple rule is also produced, by which the visiting order of outgoing edges at each vertex on the graph is determined. The rule is based on each edge's the minimum normalized slackness to the QoS requested. The proposed routing scheme extends the PNNI-type hierarchical routing framework. Note that our routing scheme is one of a few QoS-based hierarchical routing schemes that address explicitly the issue of selecting a path with multiple metrics.

• Journal of the Korea Society of Computer and Information
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• v.18 no.11
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• pp.159-165
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• 2013

This paper proposes a O(E) polynomial-time algorithm that has been devised to simultaneously solve edge-coloring problem and graph classification problem both of which remain NP-complete. The proposed algorithm selects an edge connecting maximum and minimum degree vertices so as to determine the number of edge coloring ${\chi}^{\prime}(G)$. Determined ${\chi}^{\prime}(G)$ is in turn either ${\Delta}(G)$ or ${\Delta}(G)+1$. Eventually, the result could be classified as class 1 if ${\chi}^{\prime}(G)={\Delta}(G)$ and as category 2 if ${\chi}^{\prime}(G)={\Delta}(G)+1$. This paper also proves Vizing's planar graph conjecture, which states that 'all simple, planar graphs with maximum degree six or seven are of class one, closing the remaining possible case', which has known to be NP-complete.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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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${\AA}$.