Analysis of Interconnection Networks Based on Cayley Graphs of Strong Generating Sets

Borel Cayley Graph-Based Topology Control for Consensus Protocol in Wireless Sensor Networks

ISRN Sensor Networks ◽

10.1155/2013/805635 ◽

2013 ◽

Vol 2013 ◽

pp. 1-15 ◽

Cited By ~ 2

Author(s):

Junghun Ryu ◽

Jaewook Yu ◽

Eric Noel ◽

K. Wendy Tang

Keyword(s):

Wireless Sensor Networks ◽

Sensor Networks ◽

Interconnection Networks ◽

Topology Control ◽

Cayley Graphs ◽

Small Diameter ◽

Wireless Sensor ◽

Control Algorithms ◽

Transmission Range ◽

Consensus Protocol

Borel Cayley graphs have been shown to be an efficient candidate topology in interconnection networks due to their small diameter, short path length, and low degree. In this paper, we propose topology control algorithms based on Borel Cayley graphs. In particular, we propose two methods to assign node IDs of Borel Cayley graphs as logical topologies in wireless sensor networks. The first one aims at minimizing communication distance between nodes, while the entire graph is imposed as a logical topology; while the second one aims at maximizing the number of edges of the graph to be used, while the network nodes are constrained with a finite radio transmission range. In the latter case, due to the finite transmission range, the resultant topology is an “incomplete” version of the original BCG. In both cases, we apply our algorithms in consensus protocol and compare its performance with that of the random node ID assignment and other existing topology control algorithms. Our simulation indicates that the proposed ID assignments have better performance when consensus protocols are used as a benchmark application.

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Diameter of Cayley graphs of SL(n,p) with generating sets containing a transvection

Journal of Algebra ◽

10.1016/j.jalgebra.2020.10.031 ◽

2021 ◽

Vol 569 ◽

pp. 195-219

Author(s):

Zoltán Halasi

Keyword(s):

Cayley Graphs ◽

Generating Sets

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Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions

International Journal of Foundations of Computer Science ◽

10.1142/s0129054119500278 ◽

2019 ◽

Vol 30 (08) ◽

pp. 1301-1315 ◽

Cited By ~ 1

Author(s):

Liqiong Xu ◽

Shuming Zhou ◽

Weihua Yang

Keyword(s):

Fault Tolerance ◽

Interconnection Networks ◽

Fault Tolerant ◽

Interconnection Network ◽

Cayley Graphs ◽

Disjoint Paths ◽

Local Connectivity ◽

Communication Links ◽

Restricted Condition ◽

Vertex Disjoint

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

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Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey

Parallel Computing ◽

10.1016/0167-8191(93)90054-o ◽

1993 ◽

Vol 19 (4) ◽

pp. 361-407 ◽

Cited By ~ 204

Author(s):

S Lakshmivarahan ◽

Jung-Sing Jwo ◽

S.K Dhall

Keyword(s):

Interconnection Networks ◽

Cayley Graphs ◽

Permutation Groups

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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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