• KIPS Transactions on Computer and Communication Systems
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• v.10 no.4
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• pp.93-100
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• 2021

The Ethereum shard system for solving the scalability problem of the blockchain has a load balancing issue, which is modeled as a graph partitioning problem. In this paper, we propose an adaptive online weighted graph partitioning algorithm that can negotiate between two utility of the shard system using the game theory's bargaining solution. The bargaining solution is an axiomatic solution that can fairly determine the points of conflict of utility. The proposed algorithm was improved to apply the existing online graph partitioning algorithm to the weighted graph, and load balancing was performed efficiently through the design considering the situation of the sharding system using the extension of Nash bargaining solution, which is extended to apply solution to non-convex feasible set of bargaining problem. As a result of the experiment, it showed up to 37% better performance than typical load balancing algorithm of shard system.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.171-186
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• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.12
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• pp.2410-2418
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• 2015

In this paper, we consider the femto users and their mutual interference as graph elements, nodes and weighted edges, respectively. The total bandwidth is divided into a number of resource blocks (RBs) and these are assigned to the femto user equipment (FUEs) using a graph coloring algorithm. In addition, resources blocks are assigned to the femto users to avoid inter-cell interference. The proposed scheme is compared with the traditional scheduling schemes in terms of throughput and fairness and performance improvement is achieved by exploiting the graph coloring scheme.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.115-126
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• 2016

Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

• Journal of Communications and Networks
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• v.15 no.3
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• pp.321-328
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• 2013

In this paper, we present a technique for obtaining conflict-free schedules for real-time automation protocol for industrial Ethernet (RAPIEnet) switches. Mathematical model of the switch is obtained using graph theory. Initially network traffic entry and exit parts in a single RAPIEnet switch are identified, so that a bipartite conflict graph can be constructed. The obtained conflict graph is transformed to three kinds of matrices to be used as inputs for our simulation model, and selection of any of the matrix forms is application-specific. A greedy edge-coloring algorithm is used to schedule the network traffic and to solve the minimum coloring problem. After scheduling, empty slots are identified for forwarding the non real-time traffic of asynchronous devices. Finally, an algorithm for synchronizing the schedules of adjacent switches is proposed using edge-contraction and minors. All simulations were carried out using Matlab.

• Journal of Information Science Theory and Practice
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• v.6 no.1
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• pp.18-30
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• 2018

Interest in open data is continuing to grow around the world. In particular, open government data are considered an important element in securing government transparency and creating new industrial values. The South Korean government has enacted legislation on opening public data and provided diversified policy and technical support. However, there are also limitations to effectively utilizing open data in various areas. This paper introduces an administrative district knowledge model to improve the sharing and utilization of open government data, where the data are semantically linked to generate a knowledge graph that connects various data based on administrative districts. The administrative district knowledge model semantically models the legal definition of administrative districts in South Korea, and the administrative district knowledge graph is linked to data that can serve as an administrative basis, such as addresses and postal codes, for potential use in hospitals, schools, and traffic control.

• Journal of Korea Water Resources Association
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• v.51 no.11
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• pp.989-998
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• 2018

Connectivity between water source and demand node can be served as a critical system performance indicator of the degree of water distribution network (WDN)' failure severity under abnormal conditions. Graph theory-based approaches have been widely applied to quantify the connectivity due to WDN's graph-like topological feature. However, most previous studies used undirected-unweighted graph theory which is not proper to WDN. In this study, the directed-weighted graph theory was applied for WDN connectivity analyses. We also proposed novel connectivity indicators, Source-to-Node Shortest Pathway (SNSP) and SNSP-Degree (SNSP-D) which is an inverse of the SNSP value, that does not require complicate hydraulic simulation of a WDN of interest. The proposed SNSP-D index was demonstrated in total 42 networks in J City, South Korea in which Pearson Correlation Coefficient (PCC) between the proposed SNSP-D and four other system performance indicators was computed: three resilience indexes and an energy efficiency metric. It was confirmed that a system representative value of the SNSP-D has strong correlation with all resilience and energy efficiency indexes (PCC = 0.87 on average). Especially, PCC was higher than 0.93 with modified resilience index (MRI) and energy efficiency indicator. In addition, a multiple linear regression analysis was performed to identify the system hydraulic characteristic factors that affect the correlation between SNSP-D and other system performance indicators. The proposed SNSP is expected to be served as a useful surrogate measure of resilience and/or energy efficiency indexes in practice.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.9
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• pp.1965-1970
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• 2011

This paper proposes the method of switching function implementation using switching function extraction based on graph over finite fields. After we deduce the matrix equation from path number of directional graph, we propose the switching function circuit algorithm, also we propose the code assignment algorithm for nodes which is satisfied the directional graph characteristics with designed circuits. We can implement more optimal switching function compare with former algorithm, also we can design the switching function circuit which have any natural number path through the proposed switching function circuit implementation algorithms. Also the proposed switching function implementation using graph theory over finite fields have decrement number of input-output, circuit construction simplification, increment arithmetic speed and decrement cost etc.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1145-1153
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• 2014

Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and $x,y{\in}X$ ($x{\neq}y$) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ${\Delta}(G)$. The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(${\Delta}(G)$) is abelian if and only if ${\mid}G{\mid}{\leq}2$; ${\mid}Aut({\Delta}(G)){\mid}$ is of prime power if and only if ${\mid}G{\mid}{\leq}2$, and ${\mid}Aut({\Delta}(G)){\mid}$ is square-free if and only if ${\mid}G{\mid}{\leq}3$. Some new graphs that are useful in studying the automorphism group of ${\Delta}(G)$ are presented and their main properties are investigated.

• KIEAE Journal
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• v.11 no.6
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• pp.95-100
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• 2011

Although Space Syntax is a well-known technique for spatial analysis, debates have taken place among some researchers because the Space Syntax discards geometric information as both shapes and sizes of spaces, and hence may cause some inconsistencies. Therefore, this study aims at developing methods to recognize and manage spatial shapes for more precise space syntax analysis. To reach this goal, this study employed both a graph theory and binary spatial partitioning (BSP) tree to recognize and manage spatial information. As a result, spatial shapes and sizes could be recognized by checking loops in graph converted from spatial shapes of built environment. Each spatial shape could be managed sequentially by BSP tree with hierarchical structure. Through such recognition and management processes, convex maps composed of the fattest and fewest convex spaces could be drawn. In conclusion, we hope that the methods developed here will be useful for urban planning to find appropriate purposes of spaces to satisfy the sustainability of built environment on the basis of the spatial and social relationships in urban spaces.