Interconnection Networks Based on a Generalization of Cube-Connected Cycles
IEEE Transactions on Computers
Strategies for interconnection networks: some methods from graph theory
Journal of Parallel and Distributed Computing
A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Dynamic routing for regular direct computer networks
Dynamic routing for regular direct computer networks
Vertex-transitivity and routing for Cayley graphs in GCR representations
SAC '92 Proceedings of the 1992 ACM/SIGAPP symposium on Applied computing: technological challenges of the 1990's
Representations of Borel Cayley graphs
SIAM Journal on Discrete Mathematics
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
| Hi-index | 14.98 |
Dense, symmetric graphs are useful interconnection models for multicomputer systems. Borel Cayley graphs, the densest degree-4 graphs for a range of diameters [1], are attractive candidates. However, the group-theoretic representation of these graphs makes the development of efficient routing algorithms difficult. In earlier reports, we showed that all degree-4 Borel Cayley graphs have generalized chordal ring (GCR) and chordal ring (CR) representations [2], [3]. In this paper, we present the class-congruence property and use this property to develop the two-phase routing algorithm for Borel Cayley graphs in a special GCR representation. The algorithm requires a small space complexity of O(p+k) for n=p脳k nodes. Although suboptimal, the algorithm finds paths with length bounded by 2D, where D is the diameter. Furthermore, our computer implementation of the algorithm on networks with 1,081 and 15,657 nodes shows that the average path length is on the order of the diameter. The performance of the algorithm is compared with that of existing optimal and suboptimal algorithms.