• East Asian mathematical journal
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• v.35 no.1
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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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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• v.1 no.1
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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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• v.14 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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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.

• Journal of KIISE:Databases
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• v.31 no.3
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• pp.320-330
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• 2004

Query languages for XML use paths in a data graph to represent queries. Actually, paths in a data graph are used as a basic constructor of an XML query. User can write more expressive Queries by using Patterns (e.g. regular expressions) for paths. There are many identical paths in a data graph because of the feature of semi-structured data. Current researches for indexing XML utilize identical paths in a data graph, but such an index can grow larger than source data graph and cannot guarantee efficient access path. In this paper we propose a partitioning technique that can partition all the paths in a data graph. We develop an index graph that can find appropriate partitions for a path query efficiently. The size of our index graph can be adjusted regardless of the source data. So, we can significantly improve the cost for index graph traversals. In the performance study, we show our index much faster than other graph based indexes.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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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.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.7
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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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• v.17 no.1
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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%.