Simulation of Meshes with Separable Buses by Meshes with Multiple Partitioned Buses

This paper studies the simulation problem of meshes with separable buses (MSB) by meshes with multiple partitioned buses (MMPB). The MSB and the MMPB are the mesh connected computers enhanced by the addition of broadcasting buses along every row and column. The broadcasting buses of the MSB, called separable buses, can be dynamically sectioned into smaller bus segments by program control, while those of the MMPB, called partitioned buses, are statically partitioned in advance. In the MSB model, each row/column has only one separable bus, while in the MMPB model, each row/column has L partitioned buses (L ≥ 2). We consider the simulation and the scalingsimulation of the MSB by the MMPB, and show that the MMPB of size n× n can simulate the MSB of size n× n in O(n) steps, and that the MMPB of size m×m can simulate the MSB of size n× n in O( n m ( n m + m)) steps (m < n). The latter result implies that the MMPB of size m×m can simulate the MSB of size n× n timeoptimally when m ≤ n holds for α = 1 1+1/(2L) .