• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1243-1253
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• 2008

In this paper, we construct one-factorizations of given complete graphs of even order. These constructions partition the edges of the complete graph into one-factors and triples. Our new constructions of one-factors and triples can be applied to a recursive construction of Steiner triple systems for all possible orders ${\geq}$15.

• Safety and Health at Work
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• v.12 no.1
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• pp.42-50
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• 2021

Introduction: Despite huge investments in new technology and transportation infrastructure, terrible accidents still remain a reality of traffic. Methods: Severe traffic accidents were analyzed from four prevailing modes of today's transportations: sea, air, railway, and road. Main root causes of all four accidents were defined with implementation of the approach, based on Flanagan's critical incident technique. In accordance with Molan's Availability Humanization model (AH model), possible preventive or humanization interventions were defined with the focus on technology, environment, organization, and human factors. Results: According to our analyses, there are significant similarities between accidents. Root causes of accidents, human behavioral patterns, and possible humanization measures were presented with rooted graphs. It is possible to create a generalized model graph, which is similar to rooted graphs, for identification of possible humanization measures, intended to prevent similar accidents in the future. Majority of proposed humanization interventions are focused on organization. Organizational interventions are effective in assurance of adequate and safe behavior. Conclusions: Formalization of root cause analysis with rooted graphs in a model offers possibility for implementation of presented methods in analysis of particular events. Implementation of proposed humanization measures in a particular analyzed situation is the basis for creation of safety culture.

• The Transactions of the Korea Information Processing Society
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• v.5 no.11
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• pp.2823-2834
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• 1998

This paper deals with the problem of one-to-one mapping of $2^n$ task modules of a parallel program to an n-dimensional hypercube multicomputer so as to minimize to total communication cost during the execution of the task. The problem of finding an optimal mapping has been proven to be NP-complete. We first propose a graph modification technique which transfers the mapping problem in a hypercube multicomputer into the problem of finding a set of maximum cutsets on a given task graph. Using the graph modification technique, we then propose a repeated mapping scheme which efficiently finds a one-to-one mapping of task modules to a hypercube multicomputer by repeatedly applying an existing bipartitioning algorithm on the modified graph. The repeated mapping scheme is shown to be highly effective on a number of test task graphs, it increasingly outperforms the greedy and recursive mapping algorithms as the number of processors increase. The proposed algorithm is shown to be very effective for regular graph, such as hypercube-isomorphic or 'almost' isomorphic graphs and meshes; it finds optimal mapping on almost all the regular task graphs considered.

• Journal of KIISE:Computer Systems and Theory
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• v.37 no.1
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• pp.27-34
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• 2010

Web crawlers are fundamental programs which iteratively download web pages by following links of web pages starting from a small set of initial URLs. Previously several web crawling orderings have been proposed to crawl popular web pages in preference to other pages, but some graph search techniques whose characteristics and efficient implementations had been studied in graph theory community have not been applied yet for web crawling orderings. In this paper we consider various graph search techniques including lexicographic breadth-first search, lexicographic depth-first search and maximum cardinality search as well as well-known breadth-first search and depth-first search, and then choose effective web crawling orderings which have linear time complexity and crawl popular pages early. Especially, for maximum cardinality search and lexicographic breadth-first search whose implementations are non-trivial, we propose linear-time web crawling orderings by applying the partition refinement method. Experimental results show that maximum cardinality search has desirable properties in both time complexity and the quality of crawled pages.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4703-4723
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• 2018

In recent years, dense small cell network has been deployed to address the challenge that has resulted from the unprecendented growth of mobile data traffic and users. It has proven to be a cost efficeient solution to offload traffic from macro-cells. Software defined heterogeneous wireless network can decouple the control plane from the data plane. The control signal goes through the macro-cell while the data traffic can be offloaded by small cells. In this paper, we propose a framework for cell virtualization and user association in order to satisfy versatile requirements of multiple tenants. In the proposed framework, we propose an interference graph partioning based virtual-cell association and customized physical-cell association for multi-homed users in a software defined small cell network. The proposed user association scheme includes 3 steps: initialization, virtual-cell association and physical-cell association. Simulation results show that the proposed virtual-cell association outperforms the other schemes. For physical-cell association, the results on resource utilization and user fairness are examined for mobile users and infrastructure providers.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.37-42
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• 2024

This paper suggests polynomial time algorithm for cutwidth minimization problem that classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. To find the minimum cutwidth CW_f(G)=max_𝜈∈_VCW_f(𝜈)for given graph G=(V,E),m=｜V｜, n=｜E｜, the proposed algorithm divides neighborhood N_G[𝜈_i] of the maximum degree vertex 𝜈_i in graph G into left and right and decides the vertical cut plane with minimum number of edges pass through the vertex 𝜈_i firstly. Then, we split the left and right N_G[𝜈_i] into horizontal sections with minimum pass through edges. Secondly, the inner-section vertices are connected into line graph and the inter-section lines are connected by one line layout. Finally, we perform the optimization process in order to obtain the minimum cutwidth using vertex moving method. Though the proposed algorithm requires O(n²) time complexity, that can be obtains the optimal solutions for all of various experimental data

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.4
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• pp.1712-1731
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• 2016

In this paper, we propose a novel saliency detection framework via multiple random walks (MRW) which simulate multiple agents on a graph simultaneously. In the MRW system, two agents, which represent the seeds of background and foreground, traverse the graph according to a transition matrix, and interact with each other to achieve a state of equilibrium. The proposed algorithm is divided into three steps. First, an initial segmentation is performed to partition an input image into homogeneous regions (i.e., superpixels) for saliency computation. Based on the regions of image, we construct a graph that the nodes correspond to the superpixels in the image, and the edges between neighboring nodes represent the similarities of the corresponding superpixels. Second, to generate the seeds of background, we first filter out one of the four boundaries that most unlikely belong to the background. The superpixels on each of the three remaining sides of the image will be labeled as the seeds of background. To generate the seeds of foreground, we utilize the center prior that foreground objects tend to appear near the image center. In last step, the seeds of foreground and background are treated as two different agents in multiple random walkers to complete the process of salient object detection. Experimental results on three benchmark databases demonstrate the proposed method performs well when it against the state-of-the-art methods in terms of accuracy and robustness.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.843-849
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• 2012

Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${\chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

• 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.