• Title/Summary/Keyword: Graph

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Embedding between a Macro-Star Graph and a Matrix Star Graph (매크로-스타 그래프와 행렬 스타 그래프 사이의 임베딩)

  • Lee, Hyeong-Ok
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.3
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    • pp.571-579
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    • 1999
  • A Macro-Star graph which has a star graph as a basic module has node symmetry, maximum fault tolerance, and hierarchical decomposition property. And, it is an interconnection network which improves a network cost against a star graph. A matrix star graph also has such good properties of a Macro-Star graph and is an interconnection network which has a lower network cost than a Maco-Star graph. In this paper, we propose a method to embed between a Macro-Star graph and a matrix star graph. We show that a Macro-Star graph MS(k, n) can be embedded into a matrix star graph MS\ulcorner with dilation 2. In addition, we show that a matrix star graph MS\ulcorner can be embedded into a Macro-Star graph MS(k,n+1) with dilation 4 and average dilation 3 or less as well. This result means that several algorithms developed in a star graph can be simulated in a matrix star graph with constant cost.

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A Graph Embedding Technique for Weighted Graphs Based on LSTM Autoencoders

  • Seo, Minji;Lee, Ki Yong
    • Journal of Information Processing Systems
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    • v.16 no.6
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    • pp.1407-1423
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    • 2020
  • A graph is a data structure consisting of nodes and edges between these nodes. Graph embedding is to generate a low dimensional vector for a given graph that best represents the characteristics of the graph. Recently, there have been studies on graph embedding, especially using deep learning techniques. However, until now, most deep learning-based graph embedding techniques have focused on unweighted graphs. Therefore, in this paper, we propose a graph embedding technique for weighted graphs based on long short-term memory (LSTM) autoencoders. Given weighted graphs, we traverse each graph to extract node-weight sequences from the graph. Each node-weight sequence represents a path in the graph consisting of nodes and the weights between these nodes. We then train an LSTM autoencoder on the extracted node-weight sequences and encode each nodeweight sequence into a fixed-length vector using the trained LSTM autoencoder. Finally, for each graph, we collect the encoding vectors obtained from the graph and combine them to generate the final embedding vector for the graph. These embedding vectors can be used to classify weighted graphs or to search for similar weighted graphs. The experiments on synthetic and real datasets show that the proposed method is effective in measuring the similarity between weighted graphs.

GraphSLAM Improved by Removing Measurement Outliers (측정 아웃라이어 제거를 통해 개선된 GraphSLAM)

  • Kim, Ryun-Seok;Choi, Hyuk-Doo;Kim, Eun-Tai
    • Journal of the Korean Institute of Intelligent Systems
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    • v.21 no.4
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    • pp.493-498
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    • 2011
  • This paper presents the GraphSLAM improved by selecting the measurement with respect to their likelihoods. GraphSLAM estimates the robot's path and map by utilizing the entire history of input data. However, GraphSLAM's performance suffers a lot from severely noisy measurements. In this paper, we present GraphSLAM improved by the selective measurement method. Thus the presented GraphSLAM provides higher performance compared with the standard GraphSLAM.

Embedding algorithm among star graph and pancake graph, bubblesort graph (스타 그래프와 팬케익, 버블정렬 그래프 사이의 임베딩 알고리즘)

  • Kim, Jong-Seok;Lee, Hyeong-Ok;Kim, Sung-Won
    • The Journal of Korean Association of Computer Education
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    • v.13 no.5
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    • pp.91-102
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    • 2010
  • Star graph is a well-known interconnection network to further improve the network cost of Hypercube and has good properties such as node symmetry, maximal fault tolerance and strongly hierarchical property. In this study, we will suggest embedding scheme among star graph and pancake graph, bubblesort graph, which are variations of star graph. We will show that bubblesort graph can be embedded into pancake and star graph with dilation 3, expansion 1, respectively and pancake graph can be embedded into bubblesort graph with dilation cost O($n^2$). Additionally, we will show that star graph can be embedded into pancake graph with dilation 4, expansion 1. Also, with dilation cost O(n) we will prove that star graph can be embedded into bubblesort graph and pancake graph can be embedded into star graph.

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ℂ-VALUED FREE PROBABILITY ON A GRAPH VON NEUMANN ALGEBRA

  • Cho, Il-Woo
    • Journal of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.601-631
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    • 2010
  • In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalar-valued $W^*$-probability on a given graph von Neumann algebra. We show that a diagonal graph $W^*$-probability space (as a scalar-valued $W^*$-probability space) and a graph W¤-probability space (as an amalgamated $W^*$-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility, we observe the scalar-valued freeness on a graph von Neumann algebra.

LAPLACIAN SPECTRA OF GRAPH BUNDLES

  • Kim, Ju-Young
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1159-1174
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    • 1996
  • The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

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A Half Pancake network that improve the network cost for Pancake graph (팬케익 그래프의 망비용을 개선한 하프팬케익 연결망)

  • Kim, JuBong;Seo, Jung-Hyun;Lee, HyeongOk
    • Journal of Korea Multimedia Society
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    • v.17 no.6
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    • pp.716-724
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    • 2014
  • The pancake graph is node symmetric and is utilized on the data sorting algorithm. We propose a new half pancake graph that improve pancake graph's network cost. The half pancake degree is approximately half of pancakes degree and diameter is 3n+4. The pancake graph's network cost is $O(1.64n^2)$ and half pancake's is $O(1.5n^2)$. Additionally half pancake graph is sub graph of pancake graph. As this result, The several algorithms developed in pancake graph has the advantage of leverage on the pancake by adding constant cost.

Analysis of the network robustness based on the centrality of vertices in the graph

  • Jeong, Changkwon;Han, Chi-Geun;Lee, Sang-Hoon
    • Journal of the Korea Society of Computer and Information
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    • v.22 no.3
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    • pp.61-67
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    • 2017
  • This paper analyzes the robustness of the network based on the centrality of vertices in the graph. In this paper, a random graph is generated and a modified graph is constructed by adding or removing vertices or edges in the generated random graph. And then we analyze the robustness of the graph by observing changes in the centrality of the random graph and the modified graph. In the process modifying a graph, we changes some parts of the graph, which has high values of centralities, not in the whole. We study how these additional changes affect the robustness of the graph when changes occurring a group that has higher centralities than in the whole.

BINDING NUMBER CONDITIONS FOR (a, b, k)-CRITICAL GRAPHS

  • Zhou, Sizhong
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.53-57
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    • 2008
  • Let G be a graph, and let a, b, k be integers with $0{\leq}a{\leq}b,k\geq0$. Then graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, the relationship between binding number bind(G) and (a, b, k)-critical graph is discussed, and a binding number condition for a graph to be (a, b, k)-critical is given.