An Efficient Algorithm for the k-Pairwise Disjoint Paths Problem in Hypercubes

Gu, Qian-Ping; Peng, Shietung

doi:10.1006/jpdc.2000.1632

Cited by 40 publications

(5 citation statements)

References 13 publications

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“…Besides, disjoint paths have applications in multipath routing (such as Rabin's information dispersal algorithm [23]), fault tolerance (see [3,8]), and communication protocols (see [12]). Disjoint paths in a variety of networks can be found in the literature [6,9,12,14,24]. Among them, one-to-one disjoint paths are also named containers, which we formally define in the next section.…”

Section: Introductionmentioning

confidence: 99%

Node-disjoint paths in hierarchical hypercube networks

Chen

Kuo

et al. 2007

Information Sciences

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Section: Introductionmentioning

confidence: 99%

Node-disjoint paths in hierarchical hypercube networks

Chen

Kuo

et al. 2007

Information Sciences

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“…As for different topologies, Gu and Peng described a pairwise disjoint-path routing algorithm in a hypercube [ 21 ] and in a star-graph [ 22 ]. Bossard and Kaneko solved the same problem in perfect hierarchical hypercubes [ 23 ], as did Sawada et al in pancake graphs [ 24 ], and Park focused on restricted hypercube-like graphs [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

Torus Pairwise Disjoint-Path Routing

Bossard

Kaneko

2018

Sensors

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Modern supercomputers include hundreds of thousands of processors and they are thus massively parallel systems. The interconnection network of a system is in charge of mutually connecting these processors. Recently, the torus has become a very popular interconnection network topology. For example, the Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P, and Cray Titan supercomputers all rely on this topology. The pairwise disjoint-path routing problem in a torus network is addressed in this paper. This fundamental problem consists of the selection of mutually vertex disjoint paths between given vertex pairs. Proposing a solution to this problem has critical implications, such as increased system dependability and more efficient data transfers, and provides concrete implementation of green and sustainable computing as well as security, privacy, and trust, for instance, for the Internet of Things (IoT). Then, the correctness and complexities of the proposed routing algorithm are formally established. Precisely, in an n-dimensional k-ary torus (n

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“…A comparison between BSNs and OTIS networks is shown in Table 1. One of the unsolved issues concerning BSNs is the node-to-node disjoint paths problem: for a pair of nodes s and d in a k-connected graph G=〈V,E〉, to find k paths between s and d that are node-disjoint except for s and d. Finding node-disjoint paths in interconnection networks, as one of the fundamental issues in design and implementation of parallel and distributed computing systems, are useful in speeding up the transfer of large amounts of data between nodes and in providing alternative routes in cases of node or link failures [2,5,6]. In general, the problem can be solved by using the maximum flow technique in polynomial time of the number of nodes of the graph.…”

Section: Introductionmentioning

confidence: 99%

Constructing Node-Disjoint Paths in Biswapped Networks (BSNs)

Chen

Xiao

2008

2008 the 3rd International Conference on Grid and Pervasive Computing - Workshops

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The recent biswapped networks (BSNs) offer a systematic scheme for building large, scalable, modular, and robust parallel architectures of arbitrary basis networks. BSNs are related to well-known swapped or OTIS networks, and are promising because of their attractive performance attributes including structural symmetry and algorithmic efficiency. In this paper we present an efficient general algorithm for constructing a maximal number of node-disjoint paths between two distinct nodes in a BSN built of an arbitrary basis network and analyze its performance. From this algorithm, we prove that a BSN is maximally fault tolerant if its basis network is connected. As an example application, we show that this algorithm finds the desirable node disjoint paths of length at most 1.5D+3 in O(log 3 N) time when applied to an N-node BSN of diameter D built of a cube, and also estimate the average performance concerning the maximum path length by computer simulation.

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An Efficient Algorithm for the k-Pairwise Disjoint Paths Problem in Hypercubes

Cited by 40 publications

References 13 publications

Node-disjoint paths in hierarchical hypercube networks

Node-disjoint paths in hierarchical hypercube networks

Torus Pairwise Disjoint-Path Routing

Constructing Node-Disjoint Paths in Biswapped Networks (BSNs)

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