A new class of interconnection networks based on alternating group

This paper proposes a technique to modify a Multistage Interconnection Network (MIN) to augment it with fault tolerant capabilities. The augmented MIN is referred to as Enhanced MIN (E-MIN). The technique employed for construction of E-MIN is compared with the two known physical fault tolerance techniques, namely, extra staging and chaining. EMINs are found to be more generic than extra staged networks and less expensive than chained networks. The EMIN realizes all the permutations realizable by the original MIN. The routing strategies under faulty and fault free conditions are shown to be very simple in the case of E-MINs.

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A GENERATING FUNCTION APPROACH TO THE SURFACE AREAS OF SOME INTERCONNECTION NETWORKS

Journal of Interconnection Networks ◽

10.1142/s0219265909002510 ◽

2009 ◽

Vol 10 (03) ◽

pp. 189-204 ◽

Cited By ~ 7

Author(s):

EDDIE CHENG ◽

KE QIU ◽

ZHIZHANG SHEN

Keyword(s):

Generating Function ◽

Interconnection Networks ◽

Interconnection Network ◽

Direct Consequence ◽

Alternating Group ◽

Function Technique ◽

Explicit Formulas ◽

Star Graphs ◽

Surface Areas ◽

Whitney Number

An important and interesting parameter of an interconnection network is the number of vertices of a specific distance from a specific vertex. This is known as the surface area or the Whitney number of the second kind. In this paper, we give explicit formulas for the surface areas of the (n, k)-star graphs and the arrangement graphs via the generating function technique. As a direct consequence, these formulas will also provide such explicit formulas for the star graphs, the alternating group graphs and the split-stars since these graphs are related to the (n, k)-star graphs and the arrangement graphs. In addition, we derive the average distances for these graphs.

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A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

Journal of Interconnection Networks ◽

10.1142/s0219265918500056 ◽

2018 ◽

Vol 18 (01) ◽

pp. 1850005 ◽

Cited By ~ 3

Author(s):

SHIYING WANG ◽

LINGQI ZHAO

Keyword(s):

Interconnection Networks ◽

Interconnection Network ◽

Alternating Group ◽

Multiprocessor System ◽

Multiprocessor Systems ◽

Free Node ◽

Pmc Model ◽

Important Study ◽

Communication Links ◽

Alternating Group Graph

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.

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dBCube: a new class of hierarchical multiprocessor interconnection networks with area efficient layout

IEEE Transactions on Parallel and Distributed Systems ◽

10.1109/71.250115 ◽

1993 ◽

Vol 4 (12) ◽

pp. 1332-1344 ◽

Cited By ~ 59

Author(s):

Chienhua Chen ◽

D.P. Agrawal

Keyword(s):

Interconnection Networks ◽

New Class ◽

Multiprocessor Interconnection Networks ◽

Multiprocessor Interconnection ◽

Area Efficient

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THE Qn,k,m GRAPH: A COMMON GENERALIZATION OF VARIOUS POPULAR INTERCONNECTION NETWORKS

Parallel Processing Letters ◽

10.1142/s0129626413500114 ◽

2013 ◽

Vol 23 (03) ◽

pp. 1350011 ◽

Cited By ~ 1

Author(s):

EDDIE CHENG ◽

NART SHAWASH

Keyword(s):

Interconnection Networks ◽

Cayley Graphs ◽

Alternating Group ◽

Star Graph ◽

Strong Connectivity ◽

Common Generalization ◽

Arrangement Graph ◽

Special Case ◽

Alternating Group Graph

The star graph and the alternating group graph were introduced as competitive alternatives to the hypercube, and they are indeed superior over the hypercube under many measures. However, they do suffer from scaling issues. To address this, different generalizations, namely, the (n,k)-star graph and the arrangement graph were introduced to address this shortcoming. From another direction, the star graph was recognized as a special case of Cayley graphs whose generators can be associated with a tree. Nevertheless, all these networks appear to be very different and yet share many properties. In this paper, we will solve this mystery by providing a common generalization of all these networks. Moreover, we will show that these networks have strong connectivity properties.

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Strong Matching Preclusion of Arrangement Graphs

Journal of Interconnection Networks ◽

10.1142/s0219265916500043 ◽

2016 ◽

Vol 16 (02) ◽

pp. 1650004 ◽

Cited By ~ 4

Author(s):

EDDIE CHENG ◽

OMER SIDDIQUI

Keyword(s):

Interconnection Networks ◽

Perfect Matchings ◽

Alternating Group ◽

Star Graphs ◽

Common Generalization ◽

Minimum Number

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph with neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of the star graphs and alternating group graphs, and to provide an even richer class of interconnection networks. In this paper, the goal is to find the strong matching preclusion number of arrangement graphs and to categorize all optimal strong matching preclusion sets of these graphs.

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