Optimal simulation of meshes with dynamically separable buses by meshes with statically 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 ≥ 1). We present an algorithm that simulates the MSB of size n × n in O (n¹(2L+1)/) steps using the MMPB of size n × n, and prove that the time-complexity of the algorithm is optimal in the worst case.