• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.709-717
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• 1997

For an undirected graph G=(V, E), the Rural Postman Problem (RPP) is a problem that finds a minimum cost tour that must pass edges in E'($\subseteq$ E) at least once. RPP, such as Traveling Salesman Problem (TSP), is known as an NP. Complete problem. In the previous study of RPP, he structure of the chromosome is constructed by E' and the direction of the edge. Hence, the larger the size of IE' I is, the larger the size of the chromosome and the size of the solution space are. In this paper, we transform the RPP into a Hamiltonian graph and use a genetic algorithm to solve the transformed problem using restructured chromosomes. In the simulations, we analyze our method and the previous study. From the simulation results, it is found that the results of the proposed method is better than those of the previous method and the proposed method also obtains the near optimal solution in earlier generations than the previous study.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-202
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• 2014

An element r of a commutative semiring R with identity is said to be identity-summand if there exists $1{\neq}a{\in}R$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by ${\Gamma}(R)$. It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph ${\Gamma}(R)$ are studied.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.3
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• pp.17-33
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• 2000

We consider the Steiner tree packing problem. For a given undirected graph G =(V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets(nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. The model contains exponential number of variables, but the problem can be solved using a polynomial time column generation procedure. We test the algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.

• Management Science and Financial Engineering
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• v.16 no.3
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• pp.85-93
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• 2010

Given an undirected network with a set of source-sink pairs, we are assumed to get a benefit if a pair of source and sink nodes are connected. The k-edge survivability of a network is defined as the total benefit secured after arbitrarily selected k edges are destroyed. The problem of computing k-edge survivability is known to be NP-hard and has applications of evaluating the survivability or vulnerability of a network. In this paper, we consider the k-edge survivability problem restricted to ring networks and develop an algorithm to solve it in O($n^3$|K|) time where n is the number of nodes and K is the set of source-sink pairs.

• Journal of Electrical Engineering and Technology
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• v.3 no.3
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• pp.436-443
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• 2008

This paper presents a new method for building detection and reconstruction from aerial images. In our approach, we extract useful building location information from the generated disparity map to segment the interested objects and consequently reduce unnecessary line segments extracted in the low level feature extraction step. Hypothesis selection is carried out by using an undirected graph, in which close cycles represent complete rooftops hypotheses. We test the proposed method with the synthetic images generated from Avenches dataset of Ascona aerial images. The experiment result shows that the extracted 3D line segments of the reconstructed buildings have an average error of 1.69m and our method can be efficiently used for the task of building detection and reconstruction from aerial images.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.99-108
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• 2001

In the ring loading problem with demand splitting, traffic demands are given for each pall of nodes in an undirected ring network and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the problem is to minimize the maximum load on the ring. The fastest a1gorithm to date is Myung, Kim and Tcha＇s a1gorithm that runs in Ο(n｜K｜) time where n is the number of nodes and K is the index set of the origin-destination pairs of nodes having flow traffic demands. Here we develop an a1gorithm for the ring loading problem with demand splitting that improves the rerouting step of Myung, Kim and Tcha＇s a1gorithm arid runs in Ο(min{n｜K｜, n$^2$}) time.

• Journal of information and communication convergence engineering
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• v.9 no.2
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• pp.141-149
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• 2011

We consider the problem of assigning tasks to homogeneous nodes in the distributed system, so as to minimize the amount of communication, while balancing the processors' loads. This issue can be posed as the graph partitioning problem. Given an undirected graph G=(nodes, edges), where nodes represent task modules and edges represent communication, the goal is to divide n, the number of processors, as to balance the processors' loads, while minimizing the capacity of edges cut. Since these two optimization criteria conflict each other, one has to make a compromise between them according to the given task type. We propose a new cost function to evaluate static task assignments and a heuristic algorithm to solve the transformed problem, explicitly describing the tradeoff between the two goals. Simulation results show that our approach outperforms an existing representative approach for a variety of task and processing systems.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.81-96
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• 2015

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if $H{\cap}K{\neq}1$ where 1 denotes the trivial subgroup of G. In this paper we characterize all finite groups whose intersection graphs are planar. Our methods are elementary. Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroup graph of a group, each of whose planarity was already considered before in [2, 10, 11, 12].

• Journal of IKEEE
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• v.12 no.1
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• pp.51-58
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• 2008

This paper presents a new method for building detection and reconstruction from aerial images. In our approach, we extract the useful building location information from the generated disparity map to obtain the segmentation of interested objects and thus reduce significantly unnecessary line segment extracted in low level feature extraction step. Hypothesis selection is carried out by using undirected graph in which close cycles represent complete rooftops hypotheses, and hypothesis are finally tested to contruct building model. We test the proposed method with synthetic images generated from Avenches dataset of Ascona aerial images. The experiment result shows that the extracted 3D line segments of the buildings can be efficiently used for the task of building detection and reconstruction from aerial images.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.439-444
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• 2012

In this study, we address the formation control problem of coupled unicycle-type mobile robots, each of which can interact with its neighboring robots by communicating their position outputs. Each communication link between two mobile robots is assumed to be established according to the given time-varying interconnection topology that switches within a finite set of connected fixed undirected networks and has a non-vanishing dwell time. Under this setup, we propose a distributed formation control algorithm by using the dynamics extension and feedback linearization methods, and by employing a consensus algorithm for linear multi-agent systems which provides arbitrary fast convergence rate to the agreement of the multi-agent system. Finally, the proposed result is demonstrated through a computer simulation.