The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

Parhami, Behrooz

doi:10.1016/j.ipl.2005.05.009

Cited by 16 publications

(17 citation statements)

References 7 publications

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“…Another contribution of our work is showing that an OTIS network enjoys some new desirable properties, such as maximal fault tolerance, independent of the fault tolerance of its basis network. This is fundamentally different from those results in the literature [2], [3], [9], [10] demonstrating that OTIS networks can inherit some desirable properties, such as short diameter and Hamiltonicity, from their basis networks.…”

Section: Introductioncontrasting

confidence: 99%

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Swapped (OTIS) Networks Built of Connected Basis Networks Are Maximally Fault Tolerant

Chen

Xiao

Parhami

2009

IEEE Trans. Parallel Distrib. Syst.

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Abstract-An optical transpose interconnection system (OTIS) network with n 2 nodes is a two-level swapped architecture built of n copies of an n-node basis network that constitute its clusters. A simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j, for all i 6 ¼ j) leads to regularity, modularity, packageability, fault tolerance, and algorithmic efficiency of the resulting networks. We prove that an OTIS (swapped) network with a connected basis network possesses maximal fault tolerance, regardless of whether its basis network is maximally fault tolerant. We also show how the corresponding maximal number of node-disjoint paths between two nodes of a swapped network can be algorithmically constructed in a manner that is independent of the existence and construction of node-disjoint paths within its basis network. Our results complement previous studies that show swapped networks inheriting some desirable properties (e.g., Hamiltonicity) from their basis networks. Here, we show that the swapped connectivity actually introduces a desirable property that may not exist in the basis network. Furthermore, our general result about maximal connectivity and the corresponding node-disjoint path construction for swapped networks replace a number of proofs and constructions in the literature for specific basis networks and obviate the need for proving maximal fault tolerance and dealing with node-disjoint path constructions for many other basis networks of potential practical interest. Additionally, we use our parallel path constructions to establish that the fault diameter and wide diameter of an OTIS network is no more than 4 units greater than its diameter.

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Section: Introductioncontrasting

confidence: 99%

“…Several general properties of OTIS networks have been considered [2], [10]. More recently, Parhami has established the Hamiltonicity of OTIS (swapped) networks built of Hamiltonian basis networks [9]. Fault tolerance of interconnection networks is among the properties of considerable interest in parallel and distributed computation.…”

Section: Introductionmentioning

confidence: 99%

Swapped (OTIS) Networks Built of Connected Basis Networks Are Maximally Fault Tolerant

Chen

Xiao

Parhami

2009

IEEE Trans. Parallel Distrib. Syst.

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“…, n} with i = j, are intended to model the (longer) optical connections. The resulting OTIS network is denoted by OTIS-G. Of course, an OTIS network is dependent upon its base graph G, and numerous results have been proven for both specific base graphs and classes of base graphs (see, for example, the papers [1,3,7,8,17,18,19,23] and the references therein).…”

Section: Optical Transpose Interconnection Networkmentioning

confidence: 99%

Multiswapped networks and their topological and algorithmic properties

Stewart¹

2013

Journal of Computer and System Sciences

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“…, n}, with i = j, are intended to model the (longer) optical connections. The resulting OTIS network is denoted by OTIS-G. Of course, an OTIS network is dependent upon its base graph G, and numerous results have been proven for both specific base graphs and classes of base graphs (see, for example, the papers [1,3,4,12] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A Multipath Analysis of Biswapped Networks

Xiang

Stewart

2010

The Computer Journal

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractBiswapped networks of the form Bsw(G) have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of κ + 1 vertexdisjoint paths joining any two distinct vertices in Bsw(G), where κ ≥ 1 is the connectivity of G. In doing so, we obtain an upper bound of max{2∆(G) + 5, ∆ κ (G) + ∆(G) + 2} on the (κ + 1)-diameter of Bsw(G), where ∆(G) is the diameter of G and ∆ κ (G) the κ-diameter. Suppose that we have a deterministic multipath source routing algorithm in an interconnection network G that finds κ mutually vertex-disjoint paths in G joining any 2 distinct vertices and does this in time polynomial in ∆ κ (G), ∆(G) and κ (and independently of the number of vertices of G). Our constructions yield an analogous deterministic multipath source routing algorithm in the interconnection network Bsw(G) that finds κ + 1 mutually vertex-disjoint paths joining any 2 distinct vertices in Bsw(G) so that these paths all have length bounded as above. Moreover, our algorithm has time complexity polynomial in ∆ κ (G), ∆(G) and κ. We also show that if G is Hamiltonian then Bsw(G) is Hamiltonian, and that if G is a Cayley graph then Bsw(G) is a Cayley graph.

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The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

Cited by 16 publications

References 7 publications

Swapped (OTIS) Networks Built of Connected Basis Networks Are Maximally Fault Tolerant

Swapped (OTIS) Networks Built of Connected Basis Networks Are Maximally Fault Tolerant

Multiswapped networks and their topological and algorithmic properties

A Multipath Analysis of Biswapped Networks

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