Data movement techniques for the pyramid computer
SIAM Journal on Computing
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
An Efficient Sorting Algorithm on the Multi-Mesh Network
IEEE Transactions on Computers
Some Complexity Results for Matrix Computations on Parallel Processors
Journal of the ACM (JACM)
Graph Problems on a Mesh-Connected Processor Array
Journal of the ACM (JACM)
Sorting on a mesh-connected parallel computer
Communications of the ACM
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
Wormhole Routing for Complete Exchange in Multi-Mesh
HIPC '97 Proceedings of the Fourth International Conference on High-Performance Computing
An Efficient Sorting Algorithm on the Multi-Mesh Network
IEEE Transactions on Computers
Parallel prefix computation on extended multi-mesh network
Information Processing Letters
Multi-mesh of trees with its parallel algorithms
Journal of Systems Architecture: the EUROMICRO Journal
Routing direction determination in regular networks based on configurable circuits
Future Generation Computer Systems
Cost-efficient parallel programs based on set-distributions for polynomial interpolation
Journal of Parallel and Distributed Computing
A new scalable optimal topology for multi-hop optical networks
Computer Communications
Routing direction determination in regular networks based on configurable circuits
Future Generation Computer Systems
Linear-code multicast on parallel architectures
Advances in Engineering Software
Analysis of Multi-Sort Algorithm on Multi-Mesh of Trees (MMT) architecture
The Journal of Supercomputing
OTIS-MOT: an efficient interconnection network for parallel processing
The Journal of Supercomputing
On the implementation of links in multi-mesh networks using WDM optical networks
IWDC'05 Proceedings of the 7th international conference on Distributed Computing
Polynomial interpolation on OTIS-Mesh optoelectronic computers
IWDC'04 Proceedings of the 6th international conference on Distributed Computing
A new network topology with multiple three-dimensional meshes
IWDC'04 Proceedings of the 6th international conference on Distributed Computing
On new architectures for lightwave networks
Computer Communications
Hi-index | 14.98 |
This paper introduces a new network topology, called Multi-Mesh (MM), which uses multiple meshes as the basic building blocks interconnected in a suitable manner. The proposed network consists of $n^4$ processors and is 4-regular with a diameter of $2n$. The network also contains a Hamiltonian cycle. Simple routing algorithms for point-to-point communication, one-to-all broadcast, and multicast have been described for this network. It is shown that a simple $n^2\times n^2$ mesh can also be emulated on this network in O(1) time. Several application examples have been discussed for which this network is found to be more efficient with regard to computational time than the corresponding mesh with the same number of processors. As examples, O$(n)$ time algorithms for finding the sum, average, minimum, and maximum of $n^4$ data values, located at $n^4$ different processors have been discussed. Time-efficient implementations of algorithms for solving nontrivial problems, e.g., Lagrange's interpolation, matrix transposition, matrix multiplication, and Discrete Fourier Transform (DFT) computation have also been discussed. The time complexity of Lagrange's interpolation on this network is O$(n)$ for $n^2$ data points compared to O($n^2$) time on mesh of the same size. Matrix transpose requires O$(n^{0.5}$) time for an $n \timesn$ matrix. The time for multiplying two $n\times n$ matrices is O$(n^{0.6})$ with an AT-cost of O$(n^3)$. DFT of $n$ sample points can be computed in O$(n^{0.6})$ time on this network. Papers [6], [7] show that $n^4$ data elements can be sorted on this network in $O(n)$ time.