A Unified theory of interconnection network structure
Theoretical Computer Science
The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
A graph theoretical approach to equivalence of multistage interconnection networks
Discrete Applied Mathematics
Embedding meshes in Boolean cubes by graph decomposition
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
Group action graphs and parallel architectures
SIAM Journal on Computing
On the computational equivalence of hypercube-derived networks
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Hector: A Hierarchically Structured Shared-Memory Multiprocessor
Computer - Special issue on experimental research in computer architecture
Express Cubes: Improving the Performance of k-ary n-cube Interconnection Networks
IEEE Transactions on Computers
Hamiltonian properties of grid graphs
SIAM Journal on Discrete Mathematics
Algorithms for routing around a rectangle
Discrete Applied Mathematics - Special issue: graphs in electrical engineering, discrete algorithms and complexity
The virtual path layout problem in fast networks (extended abstract)
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
Optimal emulations by butterfly-like networks
Journal of the ACM (JACM)
The layout of virtual paths in ATM networks
IEEE/ACM Transactions on Networking (TON)
Work-preserving emulations of fixed-connection networks
Journal of the ACM (JACM)
Optimal layouts on a chain ATM network
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
On Optimal Graphs Embedded into Path and Rings, with Analysis Using l1-Spheres
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Periodically Regular Chordal Rings: Generality, Scalability, and VLSI Layout
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Balancing Communication in Ring-Structured Networks
Balancing Communication in Ring-Structured Networks
Hi-index | 0.00 |
We study four augmentations of ring networks which are intended to enhance a ring's efficiency as a communication medium significantly, while increasing its structural complexity only modestly. Chordal rings add 驴shortcut驴 edges, which can be viewed as chords, to the ring. Express rings are chordal rings whose chords are routed outside the ring. Multirings append subsidiary rings to edges of a ring and, recursively, to edges of appended subrings. Hierarchical ring networks (HRN's) append subsidiary rings to nodes of a ring and, recursively, to nodes of appended subrings. We show that these four modes of augmentation are very closely related: 1) Planar chordal rings, planar express rings, and multirings are topologically equivalent families of networks with the 驴cutwidth驴 of an express ring translating into the 驴tree depth驴 of its isomorphic multiring and vice versa. 2) Every depth-d HRN is a spanning subgraph of a ${\rm depth} \hbox {-} (2d-1)$ multiring. 3) Every depth-d multiring ${\cal M}$ can be embedded into a d-dimensional mesh with dilation 3 in such a way that some node of ${\cal M}$ resides at a corner of the mesh. 4) Every depth-d HRN ${\cal H}$ can be embedded into a d-dimensional mesh with dilation 2 in such a way that some node of ${\cal H}$ resides at a corner of the mesh. In addition to demonstrating that these four augmented ring networks are grid graphs, our embedding results afford us close bounds on how much decrease in diameter is achievable for a given increase in structural complexity for the networks. Specifically, we derive upper and lower bounds on the optimal diameters of N-node depth-d multirings and HRNs that are asymptotically tight for large N and d.