A new network topology with multiple meshes

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 n²×n² 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 n⁴ 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 n² data points compared to O(n²) time on mesh of the same size. Matrix transpose requires O(n^0.5) time for an n×n. matrix. The time for multiplying two n×n matrices is O(n^0.6) with an AT-cost of O(n³). DFT of n sample points can be computed in O(n^0.6) time on this network. The previous papers show that n ⁴ data elements can be sorted on this network in O(n) time