Constructing Independent Spanning Trees on Bubble-Sort Networks

Kao, Shih-Shun; Chang, Jou–Ming; Pai, Kung-Jui; Wu, Ro-Yu

doi:10.1007/978-3-319-94776-1_1

Cited by 8 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The determination of one node's parent Time Complexity Twisted cubes [23] by rules O(nN ) Cross cubes [24] by rules O(n 2 N ) Möbius cubes [25] by rules O(nN ) Locally twisted cubes [4] by rules O(nN ) Parity cubes [26] by rules O(nN ) Hypercubes [7] by rules O(nN ) Folded hypercubes [9] by rules O(nN ) Bubble-sort networks [10] by rules AN 4 is displayed in Figure 3. The set {1, 2, 3, 4} has 24 permutations, namely 12 even permutations and 12 odd permutations.…”

Section: Interconnection Networkmentioning

confidence: 99%

“…[12]- [15]. The IST problem has been solved on several interconnection networks, including twisted cubes [23], cross cubes [24], Möbius cubes [25], locally twisted cubes [4], [5], parity cubes [26], hypercubes [7], [8], folded hypercubes [9], and bubble-sort networks [10], [11]. To the best of our knowledge, the approach of constructing ISTs in alternating group networks is still unknown.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Top-Down Construction of Independent Spanning Trees in Alternating Group Networks

et al. 2020

Self Cite

View full text Add to dashboard Cite

A set of spanning trees in a graph G is called independent spanning trees (ISTs) if they are rooted at the same vertex r, and for each vertex v( = r) in G, the two paths from v to r in any two trees share no common vertex expect for v and r. ISTs can be applied in many research fields, such as fault-tolerant broadcasting and secure message distribution in reliable communication networks. Since Cayley graphs have been widely used to design interconnection networks, constructing ISTs on cayley graphs is worth studying. The alternating group network is a subclass of Cayley graphs, and the approach of constructing ISTs in alternating group networks is still unknown. In this paper, we propose a novel and simple top-down approach for constructing ISTs in alternating group networks. The main ideas of the algorithm are to use induction to develop small trees to big trees, to use a triangle breadth-first search (TBFS) process to create a backbone of an IST, and to use breadth-first search (BFS) process to connect the rest of nodes. Compared to other methods of different interconnection networks in the literature, the uniqueness of our method is that it does not need to determine the parent of one node by any rule, on the contrary others determine that by rules. The time complexity in n-dimensional alternating group network AN n is O(n 2 × n!), where n! is twice the number of nodes of AN n ; hence it is polynomial time. We implement the algorithm in PHP and run cases from AN 3 to AN 10 . The results reveal that all spanning trees of AN 3 to AN 10 are independent and that our algorithm is accurate and efficient.

show abstract

Section: Interconnection Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Top-Down Construction of Independent Spanning Trees in Alternating Group Networks

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the past twenty years, the IST problem has been solved on several interconnection networks, including chordal rings [15], twisted cubes [3], [27], cross cubes [7], Möbius cubes [8], locally twisted cubes [5], [12], [23], parity cubes [4], [26], hypercubes [28], [30], folded hypercubes [32], star networks [17], Gaussian networks [13], bubble-sort networks [18], [19], and recursive circulant graphs with G(cd m , d) with d > 2 [31].…”

Section: Introductionmentioning

confidence: 99%

Constructing Independent Spanning Trees on Transposition Networks

2020

View full text Add to dashboard Cite

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 article, we expand the target to construct independent spanning trees to maximize the fault tolerance of transposition networks.INDEX TERMS Independent spanning trees, transposition networks, interconnection networks, Cayley graphs.

show abstract

Constructing Independent Spanning Trees in Alternating Group Networks

Huang

Hsieh

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Constructing Independent Spanning Trees on Bubble-Sort Networks

Cited by 8 publications

References 22 publications

Top-Down Construction of Independent Spanning Trees in Alternating Group Networks

Top-Down Construction of Independent Spanning Trees in Alternating Group Networks

Constructing Independent Spanning Trees on Transposition Networks

Constructing Independent Spanning Trees in Alternating Group Networks

Contact Info

Product

Resources

About