• Journal for History of Mathematics
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• v.21 no.3
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• pp.127-142
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• 2008

In this paper, we introduce four different approaches of proving Cayley formula, which counts the number of trees(acyclic connected simple graphs). The first proof was done by Cayley using recursive formulas. On the other hands the core idea of the other three proofs is the bijective method-find an one to one correspondence between the set of trees and a suitable family of combinatorial objects. Each of the three bijection gives its own generalization of Cayley formula. In particular, the last proof, done by Seo and Shin, has an application to computer science(theoretical computation), which is a typical example that pure mathematics supply powerful tools to other research fields.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.12
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• pp.209-218
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• 2012

Recently, the Field Programmable Stateful Logic Array (FPSLA) was proposed as one of the most promising system integration technologies which will extend the life of the Moore's law. This work is the first proposal of the FPSLA design automation flow, and the approaches to logic synthesis, synchronization, physical mapping, and automatic placement of the FPSLA designs. The synchronization at each gate for pipelining determines the x-coordinates of cells, and reduces the placement to 1-dimensional problems. The objective function and its gradients for the non-linear optimization of the net length and placement density have been remodeled for the reduced global placement problem. Also, a recursive algorithm has been proposed to legalize the placement by relaxing the density overflow of bipartite bin groups in a top-down hierarchical fashion. The proposed model and algorithm are implemented, and validated by applying them to the ACM/SIGDA benchmark designs. The output state of a gate in an FPSLA needs to be duplicated so that each fanout gate can be connected to a dedicated copy. This property has been taken into account by merging the duplicated nets into a hyperedge, and then, splitting the hyperedge into edges as the optimization progresses. This yields additional 18.4% of the cell count reduction in the most dense logic stage. The practicality of the FPSLA can be further enhanced primarily by incorporating into the logic synthesis the constraint to avoid the concentrated fains of gates on some logic stages. In addition, an efficient algorithm needs to be devised for the routing problem which is based on a complicated graph. The graph models the nanowire crossbar which is trimmed to be embedded into the FPSLA fabric, and therefore, asymmetric. These CAD tools can be used to evaluate the fabric efficiency during the architecture enhancement as well as automate the design.

• Journal of the Korean Association of Geographic Information Studies
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• v.7 no.1
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• pp.84-93
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• 2004

Recently, domain-specific demands with respect to practical applications and analysis scheme using spatial thematic information are increasing. Accordingly, in this study, GIS-based application program is implemented to perform spatial analysis in transportation geography with base road layer data. Using this program, quantitative estimation of circuity and accessibility, which can be extracted from nodes composed of the graph-typed network structure, in a arbitrary analysis zone or administrative boundary zone is possible. Circuity is a concept to represent the difference extent between actual nodes and fully connected nodes in the analysis zone. While, accessibility can be used to find out extent of accessibility or connectivity between all nodes contained in the analysis zone, judging from inter-connecting status of the whole nodes. In put data of this program, which was implemented in AVX executable extension using AvenueTM of ArcView, is not transportation database information based on transportation data model, but layer data, directly obtaining from digital map sets. It is thought that computation of circuity and accessibility can be used as kinds of spatial analysis functions for GIS applications in the transportation field.

• Journal of The Korea Institute of Healthcare Architecture
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• v.21 no.2
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• pp.7-15
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• 2015

Purpose: The purpose of this study is analyze linkage and spatial and structural characteristics of outpatient department and diagnosis/treatment area of geriatric hospitals based on quantitative analysis, according to function and corridor types. Methods: To examine structural characteristics and correlation of outpatient department and diagnosis/treatment area of six geriatric hospitals according to the corridor type, were systemized according to the function and corridor type and made into a j-graph, and an index was created by using space syntax to understand spatial characteristics. Results: 1) Different functional spaces are connected by a corridor, which, therefore, can be an axis of the connectivity and linkage of functional spaces and an important element in a clear hierarchy. 2) Treatment areas were disconnected from different functional spaces and, therefore, the accessibility was low. Many hospitals had an arrangement plan for treatment and diagnosis areas, and recent hospitals have segmented treatment areas within the rehabilitation space, which resulted in deeper space. 3) In terms of the level of integration, more integrated reception area meant shallower spatial depth, and deeper space for treatment and diagnosis areas. Implications: Spatial relation of outpatient department of geriatric hospitals was analyzed based on characteristics of the elderly.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.3
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• pp.63-69
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• 2012

Given art gallery P with n vertices, the maximum (sufficient) number of mobile guards is${\lfloor}n/4{\rfloor}$ for simple polygon and${\lfloor}(3n+4)/16{\rfloor}$ for simple orthogonal polygon. However, there is no polynomial time algorithm for minimum number of mobile guards. This paper suggests polynomial time algorithm for the minimum number of mobile guards. Firstly, we obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, we select vertex u with ${\Delta}(G)$ and v with ${\Delta}(G)$ in $N_G(u)$ and delete visible edges from u,v and incident edges. Thirdly, we select $w_i$ in partial graphs and select edges that is the position of mobile guards. This algorithm applies various art galley problems with simple polygons and orthogonal polygons art gallery. As a results, the running time of proposed algorithm is linear time complexity and can be obtain the minimum number of mobile guards.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.40 no.12
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• pp.9-17
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• 2003

In this paper we proposea method for estimating the bandwidth in next-generation If network. Especially, we concentrate on the edge routers accommodating the VoIP connections as well as a group of data connections. Bandwidth dimensioning is carried out at call level and packet level for voice traffic in the next-generation IP network. The model incorporates the statistical estimation approach at a call level for obtaining the number of voice connections simultaneously in the active mode. The call level model incorporates a statistical technique to compute the statistics of the number of active connections such as the mean and variance of the simultaneously connected calls in the network. The packet level model represents a load map for voice and data traffic by using non-preemptive M/G/1 queuing model with strict priority for voice over data buffer, From the proposed traffic model, we can derive a graph for upper bounds on the traffic load in terms of bandwidth for voice and data connections. Via numerical experiments we illustrate the implication of the work.

• School Mathematics
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• v.16 no.1
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• pp.83-110
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• 2014

This study analyzed the mathematics textbooks of middle grades in the first Korean curriculum, based on the modern trends of mathematics education curriculum, comparing with present Korean curriculum's other textbooks and the American textbook, MiC. The mathematics textbooks in the first Korean curriculum are based on various situations in our real life and introduce mathematical concepts throughout a set of mathematics problems. The textbooks present mathematical concepts with connected knowledge and include mathematical activities which make students use mathematical table, graph and formula at the same time. And students are actively required to discuss together during the mathematics problem solving process. As the results of this modern review on Korean 1st curriculum and middle grades mathematics textbooks, it would provide preliminary data and meaningful implications for the next curriculum and concomitant instructional materials.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.6
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• pp.165-173
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• 2012

Given a connected, weighted, and undirected graph, the Minimum Spanning Tree (MST) should have minimum sum of weights, connected all vertices, and without any cycle taking place. Borůvka Algorithm is firstly suggested as an algorithm to evaluate the MST, but it is not widely used rather than Prim and Kruskal algorithms. Borůvka algorithm selects the Minimum Weight Edge (MWE) from each vertex with distinct weights in $1^{st}$ stage, and selects the MWE from each MSF (Minimum Spanning Forest) in $2^{nd}$ stage. But the cycle check and the number of MSF in $1^{st}$ stage and $2^{nd}$ stage are difficult to implication by computer program even if it is easy to verify visually. This paper suggests the generalized Borůvka Algorithm, This algorithm selects all of the same MWEs for each vertex, then checks the cycle and constructs MSF for ascending sorted MWEs. Kruskal method bring into this process. if the number of MSF greats then 1, this algorithm selects MWE from ascending sorted inter-MSF edges. The generalized Borůvka algorithm is verified its application by being applied to the 7 graphs with the many minimum weights or distinct weight edges for any vertex. As a result, the generalized Borůvka algorithm is less required for cycle verification then the Kruskal algorithm. Therefore, the generalized Borůvka algorithm is more fast to obtain MST then Kruskal algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.83-86
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• 1996

In this paper we study the problem of augmenting a physical network to improve the topology for new survivable network architectures. We are given a graph G=(V,E,F), where V is a set of nodes that represents transmission systems which be interconnected by physical links, and E is a collection of edges that represent the possible pairs of nodes between which a direct transmission link can be placed. F, a subset of E is defined as a set of the existing direct links, and E/F is defined as a set of edges for the possible new connection. The cost of establishing network $N_{H}$=(V,H,F) is defined by the sum of the costs of the individual links contained in new link set H. We call that $N_{H}$=(V,H,F) is feasible if certain connectivity constrints can be satisfied in $N_{H}$=(V,H,F). The computational goal for the suggested model is to find a minimum cost network among the feasible solutions. For a k edge (node) connected component S .subeq. F, we charactrize some optimality conditions with respect to S. By this characterization we can find part of the network that formed by only F-edges. We do not need to augment E/F edges for these components in an optimal solution. Hence we shrink the related component into a node. We study some good primal heuristics by considering construction and exchange ideas. For the construction heuristics, we use some greedy methods and relaxation methods. For the improvement heuristics we generalize known exchange heuristics such as two-optimal cycle, three-optimal cycle, pretzel, quezel and one-optimal heuristics. Some computational experiments show that our heuristic is more efficient than some well known heuristics.stics.