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4. The 4-Component Connectivity of Alternating Group Networks

Author

Chang, Jou-Ming, Pai, Kung-Jui, Wu, Ro-Yu, and Yang, Jinn-Shyong

Subjects
Computer Science - Discrete Mathematics, Mathematics - Combinatorics
Abstract

The $\ell$-component connectivity (or $\ell$-connectivity for short) of a graph $G$, denoted by $\kappa_\ell(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a graph with fewer than $\ell$ vertices. This generalization is a natural extension of the classical connectivity defined in term of minimum vertex-cut. As an application, the $\ell$-connectivity can be used to assess the vulnerability of a graph corresponding to the underlying topology of an interconnection network, and thus is an important issue for reliability and fault tolerance of the network. So far, only a little knowledge of results have been known on $\ell$-connectivity for particular classes of graphs and small $\ell$'s. In a previous work, we studied the $\ell$-connectivity on $n$-dimensional alternating group networks $AN_n$ and obtained the result $\kappa_3(AN_n)=2n-3$ for $n\geqslant 4$. In this sequel, we continue the work and show that $\kappa_4(AN_n)=3n-6$ for $n\geqslant 4$.

Published
2018
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7. Constructing Tri-CISTs in Shuffle-Cubes

Author

Chen, Yu-Han, Pai, Kung-Jui, Lin, Hsin-Jung, Chang, Jou-Ming, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Chen, Chi-Yeh, editor, Hon, Wing-Kai, editor, Hung, Ling-Ju, editor, and Lee, Chia-Wei, editor

Published
2021
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8. Embedding Three Edge-Disjoint Hamiltonian Cycles into Locally Twisted Cubes

Author

Pai, Kung-jui, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Chen, Chi-Yeh, editor, Hon, Wing-Kai, editor, Hung, Ling-Ju, editor, and Lee, Chia-Wei, editor

Published
2021
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9. On the Orbits of Crossed Cubes

Author

Shiau, Tzong-Huei, Wang, Yue-Li, and Pai, Kung-Jui

Subjects
Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 68R10, B.2.4
Abstract

An orbit of $G$ is a subset $S$ of $V(G)$ such that $\phi(u)=v$ for any two vertices $u,v\in S$, where $\phi$ is an isomorphism of $G$. The orbit number of a graph $G$, denoted by $\text{Orb}(G)$, is the number of orbits of $G$. In [A Note on Path Embedding in Crossed Cubes with Faulty Vertices, Information Processing Letters 121 (2017) pp. 34--38], Chen et al. conjectured that $\text{Orb}(\text{CQ}_n)=2^{\lceil\frac{n}{2}\rceil-2}$ for $n\geqslant 3$, where $\text{CQ}_n$ denotes an $n$-dimensional crossed cube. In this paper, we settle the conjecture., Comment: 15 pages

Published
2017

12. A Recursive Algorithm for Constructing Dual-CISTs in Hierarchical Folded Cubic Networks.

Author

Lin, Hsin-Jung, Tang, Shyue-Ming, Pai, Kung-Jui, and Chang, Jou-Ming

Subjects
HYPERCUBES, TREE graphs, SPANNING trees, FAULT tolerance (Engineering), ALGORITHMS, DATA transmission systems
Abstract

Let = { T 1 , T 2 , ... , T k } be a set of k ≥ 2 spanning trees in a graph G. The k spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices x and y in any two trees have neither vertex nor edge in common except for x and y. Particularly, is called a dual-CIST provided k = 2. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the n -dimensional hierarchical folded cubic network H F Q n . The network is a two-level network using folded hypercube F Q n as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of H F Q n in (2 2 n) time for n ≥ 2 , where the time required is the same scale as the number of vertices of H F Q n . Also, the diameter of each constructed CIST is 4 n + 1. [ABSTRACT FROM AUTHOR]

Published
2024
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15. Designing an Algorithm to Improve the Diameters of Completely Independent Spanning Trees in Crossed Cubes

Author

Pai, Kung-Jui, Barbosa, Simone Diniz Junqueira, Editorial Board Member, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Yuan, Junsong, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Chang, Chuan-Yu, editor, Lin, Chien-Chou, editor, and Lin, Horng-Horng, editor

Published
2019
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16. Constructing Three Completely Independent Spanning Trees in Locally Twisted Cubes

Author

Pai, Kung-Jui, Chang, Ruay-Shiung, Chang, Jou-Ming, Wu, Ro-Yu, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Chen, Yijia, editor, Deng, Xiaotie, editor, and Lu, Mei, editor

Published
2019
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22. Constructing Independent Spanning Trees on Bubble-Sort Networks

Author

Kao, Shih-Shun, Chang, Jou-Ming, Pai, Kung-Jui, Wu, Ro-Yu, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Wang, Lusheng, editor, and Zhu, Daming, editor

Published
2018
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23. Two Kinds of Generalized 3-Connectivities of Alternating Group Networks

Author

Chang, Jou-Ming, Pai, Kung-Jui, Yang, Jinn-Shyong, Wu, Ro-Yu, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Chen, Jianer, editor, and Lu, Pinyan, editor

Published
2018
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26. A Parallel Construction of Vertex-Disjoint Spanning Trees with Optimal Heights in Star Networks

Author

Kao, Shih-Shun, Chang, Jou-Ming, Pai, Kung-Jui, Yang, Jinn-Shyong, Tang, Shyue-Ming, Wu, Ro-Yu, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Gao, Xiaofeng, editor, Du, Hongwei, editor, and Han, Meng, editor

Published
2017
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27. A Constant Amortized Time Algorithm for Generating Left-Child Sequences in Lexicographic Order

Author

Pai, Kung-Jui, Chang, Jou-Ming, Wu, Ro-Yu, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Xiao, Mingyu, editor, and Rosamond, Frances, editor

Published
2017
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28. Amortized Efficiency of Ranking and Unranking Left-Child Sequences in Lexicographic Order

Author

Pai, Kung-Jui, Wu, Ro-Yu, Chang, Jou-Ming, Chang, Shun-Chieh, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Chan, T-H. Hubert, editor, Li, Minming, editor, and Wang, Lusheng, editor

Published
2016
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34. A Loopless Algorithm for Generating Multiple Binary Tree Sequences Simultaneously

Author

Wu, Ro-Yu, Chang, Jou-Ming, Chan, Hung-Chang, Pai, Kung-Jui, Hutchison, David, Serieseditor, Kanade, Takeo, Serieseditor, Kittler, Josef, Serieseditor, Kleinberg, Jon M., Serieseditor, Mattern, Friedemann, Serieseditor, Mitchell, John C., Serieseditor, Naor, Moni, Serieseditor, Nierstrasz, Oscar, Serieseditor, Pandu Rangan, C., Serieseditor, Steffen, Bernhard, Serieseditor, Sudan, Madhu, Serieseditor, Terzopoulos, Demetri, Serieseditor, Tygar, Doug, Serieseditor, Vardi, Moshe Y., Serieseditor, Weikum, Gerhard, Serieseditor, Widmayer, Peter, editor, Xu, Yinfeng, editor, and Zhu, Binhai, editor

Published
2013
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