• East Asian mathematical journal
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• 제35권1호
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• pp.17-22
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• 2019

A travel groupoid is a pair (V, ${\ast}$) of a set V and a binary operation ${\ast}$ on V satisfying two axioms. For a travel groupoid, we can associate a graph in a certain manner. For a given graph G, we say that a travel groupoid (V, ${\ast}$) is on G if the graph associated with (V, ${\ast}$) is equal to G. There are some results on the classification of travel groupoids which are on a given graph [1, 2, 3, 9]. In this article, we introduce the notion of vertex-indexed partition systems on a graph, and classify the travel groupoids on the graph by the those vertex-indexed partition systems.

• 한국경영과학회지
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• 제28권4호
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• pp.131-143
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• 2003

In this paper, we present a survey about the various graph partition problems including the clustering problem, the k-cut problem, the multiterminal cut problem, the multicut problem, the sparsest cut problem, the network attack problem, the network disconnection problem. We compare those problems focusing on the problem characteristics such as the objective function and the conditions that the partitioned clusters should satisfy. We also introduce the mathematical programming formulations, and the solution approaches developed for the problems.

• 대한수학회논문집
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• 제32권1호
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• pp.183-191
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• 2017

We define a stratification and a partition of a finite topological space and define a partial order on the partition. Open subsets can be described completely in terms of this partially ordered partition. We associate a directed graph to the partially ordered partition of a finite topological space. This gives a one-to-one correspondence between finite topological spaces and a certain class of directed graphs.

• Journal of Electrical Engineering and information Science
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• 제1권1호
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• pp.164-172
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• 1996

The partitioning of related objects should be performed before clustering for an efficient access in object-oriented databases. In this paper, a horizontal partition of related objects in object-oriented databases is presented. All subclass nodes in a class inheritance hierarchy of a schema graph are shrunk to a class node in the graph that is called condensed schema graph because the aggregation hierarchy has more influence on the partition than the class inheritance hierarchy. A set function and an accessibility function are defined to find a maximal subset of related objects among the set of objects in a class. A set function maps a subset of the domain class objects to a subset of the range class objects. An accessibility function maps a subset of the objects of a class into a subset of the objects of the same class through a composition of set functions. The algorithm derived in this paper is to find the related objects of a condensed schema graph using accessibility functions and set functions. The existence of a maximal subset of the related objects in a class is proved to show the validity of the partition algorithm using the accessibility function.

• Structural Engineering and Mechanics
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• 제14권6호
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• pp.625-647
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• 2002

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

• 대한수학회지
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• 제42권4호
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• pp.847-856
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• 2005

M. Junger, G. Reinelt, and W. R. Pulleyblank asked the following questions ([2]). (1) Is it true that every simple planar 2-edge connected bipartite graph has a 3-partition in which each component consists of the edge set of a simple path? (2) Does every simple planar 2-edge connected graph have a 3-partition in which every component consists of the edge set of simple paths and triangles? The purpose of this paper is to provide a positive answer to the second question for simple outerplanar 2-vertex connected graphs and a positive answer to the first question for simple planar 2-edge connected bipartite graphs one set of whose bipartition has at most 4 vertices.

• 한국정보과학회논문지:데이타베이스
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• 제31권3호
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• pp.320-330
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• 2004

XML에 대한 질의 언어는 데이타 그래프 내의 경로를 이용하여 질의를 표현한다. 특히, 경로에 패턴 (예를 들어, 정규식)을 사용함으로써, 데이타의 구조를 정확히 알지 못하더라도 질의가 가능하도록 한다. 이때, 패턴을 이용하는 질의는 데이타 그래프의 탐색범위를 크게 넓히게 된다. 기존의 XML색인 기법은 질의의 탐색범위를 줄이기 위해 데이타 그래프 내의 서로 동일한 경로들을 하나로 묶어 작은 크기의 색인 그래프를 생성하는 방법을 이용한다. 하지만 이러한 색인들은 많은 경우 색인의 크기가 데이터 그래프의 크기만큼 증가하게 되어 질의의 탐색범위를 줄이지 못하고, 따라서 효율적인 질의 처리를 보장하지 못한다. 본 논문에서는 데이타 내에 존재하는 모든 경로를 분할(partitioning)하고 질의 처리 시 질의에 맞는 분할 영역을 빠르게 찾아낼 수 있는 색인 그래프를 제안한다. 본 논문에서 제안하는 색인 그래프는 데이터 그래프의 크기와 상관없이 색인 그래프의 크기를 조절할 수 있다. 따라서 색인 그래프의 크기를 작게 구성함으로써 색인 그래프 탐색 비용을 크게 줄일 수 있다. 본 논문에서는, 실험을 통해 기존의 그래프 기반색인 기법들보다 본 논문의 색인 기법이 보다 효율적임을 보이고 색인의 크기 변화에 따른 성능 변화에 대해 알아본다.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.

• 대한전자공학회논문지
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• 제27권7호
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• pp.1025-1032
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• 1990

We proposed a neural network energy function for the optimal graph partitioning and its optimization method using Boltzmann Machine. We composed a Boltzmann Machine with the proposed neural network energy function, and the simulation results show that we can obtain an optimal solution with the energy function parameters of A=50, B=5, c=14 and D=10, at the Boltzmann Machine parameters of To=80 and \ulcorner0.07 for a 6-node 3-partition problem. As a result, the proposed energy function and optimization parameters are proved to be feasible for the optimal graph partitioning.

• JSTS:Journal of Semiconductor Technology and Science
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• 제17권1호
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• pp.1-6
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• 2017

This paper presents an optimized adoption of NVM for the storage system of heterogeneous applications. Our analysis shows that a bulk of I/O does not happen on a single storage partition, but it is varied significantly for different application categories. In particular, journaling I/O accounts for a dominant portion of total I/O in DB applications like OLTP, whereas swap I/O accounts for a large portion of I/O in graph visualization applications, and file I/O accounts for a large portion in web browsers and multimedia players. Based on these observations, we argue that maximizing the performance gain with NVM is not obtained by fixing it as a specific storage partition but varied widely for different applications. Specifically, for graph visualization, DB, and multimedia player applications, using NVM as a swap, a journal, and a file system partitions, respectively, performs well. Our optimized adoption of NVM improves the storage performance by 10-61%.