Parallel construction of independent spanning trees and an application in diagnosis on Möbius cubes

Cheng, Baolei; Fan, Jianxi; Jia, Xiaohua; Jia, Juncheng

doi:10.1007/s11227-013-0883-1

Cited by 34 publications

(20 citation statements)

References 36 publications

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“…Our algorithm is a distributed local algorithm, so all the following G * 's are constructed on some local graphs LG(u). (Cheng et al, 2013) The crossed cube CQ 1 is a complete graph with two vertices labeled by 0 and 1, respectively. For n ≥ 2, an n-dimensional crossed cube CQ n consists of two (n − 1)-dimensional sub-crossed cubes, CQ …”

Section: Definition 5 (Square Of a Graph (Gmentioning

confidence: 99%

“…So, reducing the size of a CDS is our purpose in this paper. The crossed cube (Cheng et al, 2013) is an important class of variants of hypercubes as rule networks, which is proven to be superior to the hypercube counterpart, since it can reduce the diameter of the network. However, no result has been reported on constructing the CDS by using a crossed cube.…”

Section: Introductionmentioning

confidence: 99%

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An efficient connected dominating set algorithm in WSNs based on the induced tree of the crossed cube

Zhang

Zhou

et al. 2015

International Journal of Applied Mathematics and Computer Science

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The connected dominating set (CDS) has become a well-known approach for constructing a virtual backbone in wireless sensor networks. Then traffic can forwarded by the virtual backbone and other nodes turn off their radios to save energy. Furthermore, a smaller CDS incurs fewer interference problems. However, constructing a minimum CDS is an NP-hard problem, and thus most researchers concentrate on how to derive approximate algorithms. In this paper, a novel algorithm based on the induced tree of the crossed cube (ITCC) is presented. The ITCC is to find a maximal independent set (MIS), which is based on building an induced tree of the crossed cube network, and then to connect the MIS nodes to form a CDS. The priority of an induced tree is determined according to a new parameter, the degree of the node in the square of a graph. This paper presents the proof that the ITCC generates a CDS with a lower approximation ratio. Furthermore, it is proved that the cardinality of the induced trees is a Fibonacci sequence, and an upper bound to the number of the dominating set is established. The simulations show that the algorithm provides the smallest CDS size compared with some other traditional algorithms.

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Section: Definition 5 (Square Of a Graph (Gmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient connected dominating set algorithm in WSNs based on the induced tree of the crossed cube

Zhang

Zhou

et al. 2015

International Journal of Applied Mathematics and Computer Science

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“…., (n − 1)-neighbor). A circular dimensional-permutation (CDP for short) is a type of permutation to put all integers from 0 to n − 1 along a closed circle in the clockwise order [6]. Suppose that {a 0 , a 1 , .…”

Section: Definition Of Dimensional-permutationmentioning

confidence: 99%

“…Independent spanning trees(ISTs for short) have been used in reliable broadcasting, secure message distribution [2], reliable communication protocols [17], one-to-all broadcasting [26], the multi-node broadcasting [3], and diagnosis [6]. Therefore, the problem to construct ISTs for a given network is becoming an important issue.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, researchers are interested in the study of ISTs for various special networks. Conjecture 1 has been solved for some restricted classes of networks, such as planar networks [15], product networks [23], hypercubes [25], [28], [30], Möbius cubes [5], [6], locally twisted cubes [22], crossed cubes [4], [7], twisted cubes [27], even networks [18], odd networks [19], and etc.…”

Section: Introductionmentioning

confidence: 99%

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Circular Dimensional-Permutations and Reliable Broadcasting for Hypercubes and Möbius Cubes

Cheng

Fan

Yang

et al. 2013

Lecture Notes in Computer Science

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Abstract. Reliable broadcasting for interconnection networks can be achieved by constructing multiple independent spanning trees(ISTs) rooted at the same node. In this paper, we prove that there exists (n−1)! sets of ISTs rooted at an arbitrary node for Qn and Mn based on circular dimensional-permutations of 0, 1, . . . , n − 1 and n ≥ 1. At the same time, we give an parallel algorithm, called BCIST, which is the further study of IST problem for Qn and Mn in literature. Furthermore, simulation experiments of ISTs based on JUNG framework and different sets of disjoint paths between node 1 and any node v ∈ V (0-M4)\{1} for 0-M4 are also presented.

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A t/k diagnosis algorithm on hypercube‐like networks

Xie

Liang

2017

Concurrency and Computation

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SummaryProcessor fault diagnosis takes a key role in fault-tolerant computing on multiprocessor systems.The t∕k diagnosis strategy which is a generalization of the precise and pessimistic diagnosis strategies can significantly improve the self-diagnosing capability of the system. Using this tool, it is possible to deal with large faults in the system. This paper presents a t∕k diagnosis algorithm on n-dimensional hypercube-like networks (include Hypercubes, Crossed cubes, Möbius cubes, Locally Twisted cubes, and Twisted cubes) for any k ∈ [0, n − 2]. The algorithm can correctly identify all nodes except at most k nodes undiagnosed. It runs in O(N) time, where N = 2 n is the total number of nodes of n-dimensional hypercube-like networks. To the best of our knowledge, in the case k ≥ 4, there is no known t∕k diagnosis algorithm for general diagnosable system or any specific system. KEYWORDShypercube-like networks, large connected component, system-level diagnosis, t∕k diagnosis strategy INTRODUCTIONWith the rapid development of very large scale integration (VLSI) technology, a multiprocessor system may contain hundreds or even thousands of processors (nodes). As the number of processors increases, so does the expected number of processors being faulty at the same time. To ensure reliability, the system should have the ability to identify the faulty processors which are then isolated from the system or replaced by additional fault-free ones. The technique of identifying faulty processors by conducting tests on the processors and interpreting the test outcomes is known as system-level diagnosis.Preparata et al. 1 proposed the first model of system-level diagnosis, known as the PMC model. It assumes that each node in a system can conduct tests on its neighbors via the communication links between them. When a node tests its neighbor, the tester declares the tested node to be fault-free or faulty based on the test responses. This evaluation is reliable if and only if the testing node is fault-free.There are two classical diagnosis strategies, i.e., the precise diagnosis strategy 1 and the pessimistic diagnosis strategy. 2,3 However, due to their limited diagnosability, they are unable to deal with large faults in large multiprocessor systems. In order to greatly enhance the degree of diagnosability, Somani and Peleg proposed a new diagnosis strategy known as the t∕k diagnosis. 4 Under this strategy, all the faulty nodes can be isolated to within a set in which at most k nodes is fault-free. Specifically, a system S of N nodes is t∕k-diagnosable if, given any test syndrome produced by the system under the presence of a fault set F, all the faulty nodes can be isolated to within a set F ′ , out of which at most k nodes can possibly be fault-free, |F ′ | ≤ |F| + k, provided the number of faulty nodes does not exceed t. By definition, if k = 0, the t∕k diagnosis reduces to the precise diagnosis; if k = 1, the t∕k diagnosis is closely related to the pessimistic diagnosis. By choosing a larger k, the t∕k diagnosis can signif...

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Parallel construction of independent spanning trees and an application in diagnosis on Möbius cubes

Cited by 34 publications

References 36 publications

An efficient connected dominating set algorithm in WSNs based on the induced tree of the crossed cube

An efficient connected dominating set algorithm in WSNs based on the induced tree of the crossed cube

Circular Dimensional-Permutations and Reliable Broadcasting for Hypercubes and Möbius Cubes

A t/k diagnosis algorithm on hypercube‐like networks

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