Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks

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

doi:10.1007/s10878-019-00430-0

Cited by 17 publications

(9 citation statements)

References 28 publications

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“…Since this conjecture is still unsolved for the general k-connected graphs of k ≥ 5, the follow-up researchers mainly focused on the study of constructing multiple ISTs on specific interconnection networks under applications-driven. For instance, the construction of ISTS on some variations of hypercubes [3], [22], [32], [33], [40], torus networks [31], recursive circulant graphs [37], [38], and special subclasses of Cayley networks [7], [17], [18], [20], [21]. In particular, special topics related to IST include the research on reducing the height of ISTs [34], [36], [39] and parallel construction of ISTs [4]- [6], [35], [40], [41].…”

Section: Introductionmentioning

confidence: 99%

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

et al. 2021

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Section: Introductionmentioning

confidence: 99%

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

et al. 2021

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“…I NTERCONNECTION networks are used to be modeled by an undirected graph where a vertex represents a processor and an edge represents a communication channel. The spanning tree under a topology includes every vertex and connects without loops, massive applications [1]- [5] applied spanning tree structure to build efficient algorithms and solve related research problems. A set of spanning trees are said to be independent if they are rooted at the same root and for each of the remaining vertices there exists internally disjoint paths connect to the root.…”

Section: Introductionmentioning

confidence: 99%

Constructing Independent Spanning Trees on Generalized Recursive Circulant Graphs

2021

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The generalized recursive circulant networking can be widely used in the design and implementation of interconnection networks. It consists of a series of processors, each is connected through bidirectional, point-to-point communication channels to different neighbors. In this work, we apply the shortest path routing concept to build independent spanning trees on the generalized recursive circulant graphs. The proposed strategy loosen the restricted conditions in previous research and extended the result to a more general vertex setting by design the specific algorithm to deal with the constraint issue.

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“…[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%

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

et al. 2020

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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.

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Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks

Cited by 17 publications

References 28 publications

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

Constructing Independent Spanning Trees on Generalized Recursive Circulant Graphs

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

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