Optimum Broadcasting Algorithms in (n, k)-Star Graphs Using Spanning Trees

Li, Jinli; Chen, Manli; Xiang, Yang; Yao, Shao-Wen

doi:10.1007/978-3-540-74784-0_23

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…= Ω(k log n). Several broadcast algorithms for (n, k)-star graph have been studied [5,16,14]. Among them, in [14], an optimal time algorithm is proposed by using the neighborhood broadcasting.…”

Section: Broadcast Algorithm On the Single-port Modelmentioning

confidence: 99%

Routing and Broadcasting Algorithms for Generalized-Star Cube

Arai

2016

IJNC

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In this paper, another version of the star cube called the generalized-star cube, GSC(n, k, m), is presented as a three level interconnection topology. GSC(n, k, m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star graph with an m-cube. Because there are three parameters m, n, and k, the network size of GSC(n, k, m) can be changed more flexibly than the star graph, star-cube, and (n, k)-star graph. We first investigate the topological properties of the GSC(n, k, m), such as the node degree, diameter, average distance, and cost. Also, the regularity and node symmetry of the GSC(n, k, m) are derived. Next, we present a formal shortest-path routing algorithm. Then, we give broadcasting algorithms for both of the single-port and all-port models. To develop these algorithms, we use the spanning binomial tree, the neighborhood broadcasting algorithm, and the minimum dominating set. The complexities of the routing and broadcasting algorithms are also examined.

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Section: Broadcast Algorithm On the Single-port Modelmentioning

confidence: 99%

Routing and Broadcasting Algorithms for Generalized-Star Cube

Arai

2016

IJNC

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“…The broadcasting problem is NP-complete for 3-regular planar graphs and a constant deadline k ≥ 2 [ 27 ]. This problem is studied almost on all kinds of architectures and systems for example, wireless sensor networks [ 28 ], cellular networks of triangular systems [ 29 ], heterogeneous tree networks [ 30 ], honeycomb networks [ 31 ], higher dimensional hexagonal networks [ 32 ], mesh architectures [ 33 ], star graphs [ 34 ], de Bruijn Networks [ 35 ], hypercubes [ 36 ].…”

Section: Broadcasting Problem Of Carbon and Boron Nanotubesmentioning

confidence: 99%

Computational Aspects of Carbon and Boron Nanotubes

Manuel

2010

Molecules

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Carbon hexagonal nanotubes, boron triangular nanotubes and boron α-nanotubes are a few popular nano structures. Computational researchers look at these structures as graphs where each atom is a node and an atomic bond is an edge. While researchers are discussing the differences among the three nanotubes, we identify the topological and structural similarities among them. We show that the three nanotubes have the same maximum independent set and their matching ratios are independent of the number of columns. In addition, we illustrate that they also have similar underlying broadcasting spanning tree and identical communication behavior.

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“…S n,k has better scalability and it preserves many attractive properties of S n , such as node symmetry, distance, diameter, hierarchical structure, and fault-free shortest routing [1,4,12]. Recent research results on broadcasting [11], topological properties [5], fault-tolerant connectivity [9,15] and weak-vertex-pancyclicity [3] demonstrate that S n,k is a very powerful network.…”

Section: Introductionmentioning

confidence: 99%

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

Chiu

Huang

Yang

et al. 2014

Int. J. Found. Comput. Sci.

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The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. In the preliminary version of this paper, we built the probabilistic safety vector (PSV) with modified cycle patterns and developed the routing algorithm to decide the fault-free routing path with the help of PSV. Afterwards, we observed that the routing performance of PSV gets worse as the percentage of fault nodes increases, especially it exceeds 25%. In order to improve the routing performance with more faulty nodes, an adaptive method of threshold assignment for the PSV is also proposed. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, PSV with dynamic threshold gets the best performance in the simulations.

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Optimum Broadcasting Algorithms in (n, k)-Star Graphs Using Spanning Trees

Cited by 8 publications

References 4 publications

Routing and Broadcasting Algorithms for Generalized-Star Cube

Routing and Broadcasting Algorithms for Generalized-Star Cube

Computational Aspects of Carbon and Boron Nanotubes

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

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