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Дисертації з теми "Independent Spanning Trees"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

Avram, Florin, and Dimitris J. Bertsimas. "The Minimum Spanning Tree Constant in Geometrical Probability and Under the Independent Model; A Unified Approach." Massachusetts Institute of Technology, Operations Research Center, 1990. http://hdl.handle.net/1721.1/5189.

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Given n uniformly and independently points in the d dimensional cube of unit volume, it is well established that the length of the minimum spanning tree on these n points is asymptotic to /3MsT(d)n(d-l)/d,where the constant PMST(d) depends only on the dimension d. It has been a major open problem to determine the constant 3MST(d). In this paper we obtain an exact expression of the constant MST(d) as a series expansion. Truncating the expansion after a finite number of terms yields a sequence of lower bounds; the first 3 terms give a lower bound which is already very close to the empirically es

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2

Wang, Jhen-Ding, and 王溱鼎. "Independent Spanning Trees on Crossed Cubes." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/59244316344879651711.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>102<br>A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v(≠r), the paths from v to r in any two trees are node-disjoint except the two end nodes v and r. For an n-connected graph, the independent spanning trees problem asks to construct n ISTs rooted at an arbitrary node of the graph. Recently, Zhang et al. [Y.-H. Zhang, W. Hao, and T. Xiang, Independent spanning trees in crossed cubes, Information Processing Letters, 113 (2013) 653–658] proposed an algorithm to

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3

Lin, Bo-yen, and 林伯岩. "The Independent Spanning Trees of Torus." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/11833018537185261805.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>90<br>The study on independent spanning trees finds applications in fault-tolerant protocols for distributed computing networks. For example, the broadcasting in a network is sending a message from a given node to all other nodes in the network. We can design a fault-tolerant broadcasting scheme based on independent spanning trees [2] [8]. The fault-tolerance can be achieved by sending k copies of the message along k independent spanning trees rooted at the source node. If the source node is faultless, this scheme can tolerate up to k-1 faulty nodes. Two-dimension to

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4

Yang, Jinn-shyong, and 楊進雄. "Independent Spanning Trees on Some Interconnection Networks." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/97253205773167631658.

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博士<br>國立臺灣科技大學<br>資訊管理系<br>95<br>The vertex set and the edge set of a graph G are denoted by V (G) and E(G), respectively.Two paths P and Q connecting a vertex x to a vertex y are said to be internally disjoint, denoted by P||Q. A tree T is called a spanning tree of a graph G if V (T) = V (G). Further, T is a rooted spanning tree if it provides a specified vertex called the root of T. Let x and y be two vertices in T. We denote T[x, y] as the unique path from x to y in T. Two spanning trees T and T0 of a graph G are said to be independent if they are rooted at the same vertex, say r, and such

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5

MengYu-Lin and 林孟玉. "Independent Spanning Trees on Recursive Circulant Graphs." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/94651256289912105016.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>91<br>Two spanning trees of a given graph G = (V, E) are said to be independent if they are rooted at the same vertex, say r, and for each vertex v Î V\{r} the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. Zehavi and Itai conjectured that any k-connected graph has k independent spanning trees rooted at an arbitrary vertex. This conjecture is still open for k > 3. Broadcasting in a distributed system is the message dissemination from a source no

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6

Yao, Sing-Chen, and 姚星辰. "Completely independent spanning trees on chordal rings." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/66628288254938285812.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>101<br>Let T1,T2,...,Tk be spanning trees in a graph G. If, for any two vertices u,v of G, the paths joining u and v on the k trees are mutually vertex-disjoint, then T1,T2,...,Tk are called completely independent spanning trees in G. The construction of completely independent spanning trees can be applied in fault-tolerant broadcasting and secure message distribution on interconnection networks. Hasunuma first introduced the concept of completely independent spanning trees and conjectured that there are k completely independent spanning trees in any 2k-connec

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7

Chih-TeChan and 詹智德. "Constructing Independent Spanning Trees on Pancake Network." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/z356kd.

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碩士<br>國立成功大學<br>資訊工程學系<br>107<br>For any graph G, the set of independent spanning trees (ISTs) is defined as the set of spanning trees in $G$. All ISTs have the same root, paths from the root to another vertex between distinct trees are vertex-disjoint and edge-disjoint. The construction of multiple independent trees on a graph has numerous applications, such as fault-tolerant broadcasting and secure message distribution. The pancake graph is a subclass of Cayley graphs and since Cayley graphs are crucial for designing interconnection networks, constructing ISTs on these graphs is necessary fo

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8

Chien-FuLin and 林建夫. "Constructing Independent Spanning Trees on Transposition Network." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/twky2p.

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碩士<br>國立成功大學<br>資訊工程學系<br>107<br>In interconnection networks, data distribution and fault tolerance are crucial services. This study proposes an effective algorithm for improving connections between networks. Transposition networks are a type of Cayley graphs and have been widely used in current networks. Whenever any connection node fails, users want to reconnect as rapidly as possible, it is urgently in need to construct a new path. Thus, searching node-disjoint paths is crucial for finding a new path in networks. In this thesis, we expand the target to construct independent spanning trees t

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9

Yang, Sheng Feng, and 楊昇峰. "On the Independent Spanning Trees of Bi-Rotator Graph." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/28121247306385394702.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>92<br>Rotator graphs, first proposed by Corbett in 1994, have been studied in recent years. Later, traditional rotator graphs were modified by adding generation functions to make all edges bi-directional called bi-rotator graphs. Like star graphs, Bi-Rotator graphs also possess rich structure properties, such as symmetry, low diameter and recursive construction. This thesis focuses on the problems of constructing independent spanning trees for a given scale of the bi-rotator graphs. A bi-rotator graph of scale n contains n! nodes and degree of each node

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10

Xiao-QiangChen and 陳小強. "Constructing Independent Spanning Trees on (n,k)-Star Graphs." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/rjh72w.

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11

Lin, Jia-Cian, and 林嘉倩. "A Study of Independent Spanning Trees on Locally Twisted Cubes." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/13622048316921333626.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>98<br>Fault-tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple spanning trees with a specific property in the underlying graph of a network to serve as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and of security. The fault-tolerance can be achieved by sending k copies of the message and the security can be achieved by sending k parts of the message along the k spanning tree rooted at the source node. Recently, constru

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12

Lee, Jing Xian, and 李景賢. "On the Height of Independent Spanning Trees in Chordal Rings." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/38433681387492428102.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>89<br>Due to the innovation of information technology, the age of networking has come. The quality of a network depends on the topology of the network. The ring network that is easily implemented has become one of popular networks. The chordal ring with degree of 4 is a variation of ring network. By adding extra two links, the reliability and fault-tolerance of the network are enhanced. Furthermore the transmission delay of the network is reduced. A chordal ring, denoted by CR(N,d), is a graph G=(V,E) with V={0,1,…,N-1} and E={(u,v)|[v-u]N=1 or d}, where 2

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13

Chang, Hung-Yi, and 張弘毅. "A Preliminary Study of the Completely Independent Spanning Trees Problem." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/72815503610513323645.

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碩士<br>國立臺北商業大學<br>資訊與決策科學研究所<br>103<br>In a graph G, a set of spanning trees are said to be completely independent if for any vertices u and v, the paths connecting them on the spanning trees have neither vertex nor edge in common, except u and v. In this thesis, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n - 2, then there are ⌊ n/3 ⌋ completely independent spanning trees. Also, we show that there are two completely independent spanning trees on chordal rings CR(N,d), where N ≥ 5 and d = ⌈ N/2 ⌉ -1 or both N and d are even integers.

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14

HSIU-CHUAN, CHEN, and 陳秀娟. "Parallel Construction of Independent Spanning Trees on Generalized Honeycomb Tori." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/67160254173801405585.

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碩士<br>國立臺北商業大學<br>資訊與決策科學研究所<br>103<br>Two spanning trees of a given network are said to be independent if they are rooted at the same node, say r, and for each node v≠r two different paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees of the network is said to be independent if they are pairwise independent. The independent spanning trees (IST for short) problem has applications in fault-tolerance broadcasting and secure message distribution. It is equivalent to the one-to-many routing problem of a given network. That is, constructing multiple IST rooted

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15

Chang, Yu-Huei, and 張玉輝. "Constructing Independent Spanning Trees on Locally Twisted Cubes in Parallel." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/38064489466544905074.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>102<br>Let LTQn denote the n-dimensional locally twisted cube. Hsieh and Tu [S.-Y. Hsieh and C.-J. Tu, Constructing edge-disjoint spanning trees in locally twisted cubes, Theoretical Computer Science, 410 (2009) 926{932] presented an algorithm to construct n edge-disjoint spanning trees rooted at vertex 0 in LTQn. Later on, Lin et al. [J.-C. Lin, J.-S. Yang, C.-C. Hsu, and J.-M. Chang, Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes, Information Processing Letters, 110 (2010) 414{419] proved that Hsieh and Tu's spanning tre

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16

Liu, Yi-Jiun, and 劉宜君. "Constructing independent spanning trees for hypercubes and locally twisted cubes." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/20919339127141912268.

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碩士<br>國立交通大學<br>應用數學系所<br>97<br>The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages such as the increase of fault-tolerance and bandwidth. Thus the designs of multiple ISTs in several classes of networks have been widely investigated. In [27], Zehavi and Itai stated two versions of the n independent spanning trees conjecture. The vertex (edge) conjecture is that any n-connected ($n$-edge-connected) graph has n vertex-ISTs (edge-ISTs) rooted at an arbitrary vertex r. In [16], Khuller and Schieber proved that the vertex conjectu

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17

Luo, Sih-Syuan, and 駱思瑄. "Improving the Height of Independent Spanning Trees on Folded Hyper-Stars." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/10913387859515731695.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>102<br>Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyper-stars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning trees (ISTs) has numerous applications in networks such as fault-tolerant broadcasting and secure message distribution. In 2010, Yang and Chang [J.-S. Yang and J.-

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18

KAO, SHIH SHUN, and 高士舜. "Constructing Independent Spanning Trees on Star Networks and Bubble-Sort Networks." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/hbmsmh.

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碩士<br>國立臺北商業大學<br>資訊與決策科學研究所<br>106<br>A set of spanning trees in a graph G is called ndependent spanning trees (ISTs for short) if they are rooted at the same vertex, say r, and for each vertex v(≠ r) in G, the two paths from v to r in any two trees, say P1 and P2, satisfy E(P1) ∩ E(P2) = ∅ and V (P1) ∩ V (P2) = {v,r}. Constructing ISTs has applications on fault-tolerant broadcasting and secure message distribution in reliable communication networks. Since Cayley graphs have been used extensively to design interconnection networks, the study of constructing ISTs on Cayley graphs is very signi

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19

Meng-Ru, Wu, and 吳孟儒. "A Fully Parallelized Scheme of Constructing Independent Spanning Trees on Möbius Cubes." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/nxxa9e.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>102<br>A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v (≠ r), the paths from v to r in any two trees are node-disjoint except the two end nodes v and r. Zehavi et al. conjectured that for any n-connected graph there exist n ISTs rooted at an arbitrary node. In 2013, Cheng et al. [B. Cheng, J. Fan, X. Jia, S. Zhang, and B. Chen, Constructive algorithm of independent spanning trees on Möbius cubes, Comput. J., 56 (2013) 1347–1362] and [B. Cheng, J. Fan, X. Jia,

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20

Lin, Wen-Yen, and 林文彥. "A study of construction of independent spanning trees in hierarchical crossed cube." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/45187393768272634986.

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碩士<br>國立東華大學<br>資訊工程學系<br>103<br>A topology of a interconnection network is usually denoted by a graph where nodes represent processors and edges represent links between processors. A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v(≠r), the paths from v to r in any two trees are node disjoint except the two end nodes v and r. For an n-connected graph, the independent spanning trees problem asks to construct n ISTs rooted at an arbitrary node of the graph. Recently, Wang et al. proposed an algori

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21

Yang, Ting-Jyun, and 楊廷鈞. "A Simple Parallel Algorithm for Constructing Independent Spanning Trees on Twisted Cubes." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/69132851341891248328.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>102<br>In 1989, Zehavi and Itai [ Three tree-paths, J. Graph Theory, (1989) ] proposed the following conjecture: a k-connected graph G must possess k independent span- ning trees (ISTs for short) with an arbitrary node as the root. An n-dimensional twisted cube, denoted by TQn, is a variation of hypercubes with connectivity n to achieving some improvements of structure properties. 2010, Yang [ Constructing edge-disjoint spanning trees in twisted cubes Inform. Sci., (2010) ] proposed an al- gorithm for constructing n edge-disjoint spanning trees in TQn for any

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22

Kuo, Chi-Jung, and 郭啟容. "On the Study of Feedback Problems and Independent Spanning Trees in Cayley Graphs." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/07750723911737262248.

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博士<br>國立臺灣科技大學<br>資訊管理系<br>98<br>Rotator graph and trivalent Cayley graph are two members of Cayley graphs. This dissertation studies the minimum feedback vertex/arc set in rotator and incomplete rotator graphs, as well as the independent spanning trees of trivalent Cayley graphs. A feedback vertex/arc set (abbreviated as FVS/FAS) of a graph is a subset of the vertices/arcs which contains at least one vertex/arc for every cycle of the graph. Removing the FVS/FAS from the graph makes the remaining graph acyclic. A minimum FVS/FAS is an FVS/FAS which contains the smallest number of vertices/arcs

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23

Ke, Bo-Ren, and 柯博仁. "An advanced study of construction of independent spanning trees for Hierarchical Crossed Cubes:." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/88319608550474540597.

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碩士<br>國立東華大學<br>資訊工程學系<br>104<br>A topology of a interconnection network is usually denoted by a graph where nodes represent processors and edges represent links between processors. If all the trees are rooted at the same node r and for any other node v(̸= r), the paths from v to r in any two trees are node disjoint except the two end nodes v and r, a set of spanning trees in a graph is said to be independent (ISTs for short). The independent spanning trees for data broadcasting in networks provide a number of advantages that included the increase of fault-tolerance and bandwidth. Hierarchical

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24

CHIH, WU HSIEN, and 吳先智. "Improve the Height of Independent Spanning Trees and Point-to-Point Parallel Routing in Chordal Rings." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/33852948752821493645.

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碩士<br>國立臺灣科技大學<br>資訊管理系<br>90<br>Due to the innovation of information technology, the age of networking has come. The quality of some network depends on the topology of the network. The ring network that is easily implemented has become a popular network. The chordal ring with degree of 4 is a variation of ring network. By adding extra two links for each vertex, the reliability and fault-tolerance of the network are enhanced. Furthermore, the transmission delay of the network is reduced. A chordal ring, denoted by CR(N,d), can be represented by a graph G=(V,E) with V={0,1,…,N-1} and

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25

Chi, Ping-Hsien, and 紀秉賢. "Examing the Completely Independent Spanning Tree under the Frame Work of Open Source MapReduce." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/33686273717161574306.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>101<br>Cloud computing is not a new network technology, but a new concept of the network. By the network of cooperating the different computers and the concept of the Internet to generate the corresponding technology, essentially, from the dis- tributed computing and grid computing. Distributed computing is a work into many small works, and then were assigned to more than one computer to complete the work of stand-alone, and finally collected all results. Grid computing is an extension of distributed computing, the main features are different platforms, level-

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